Gemara

(Rav Ashi): Pigul is not established until Zerikah. (When the intents make Pigul,) it takes effect retroactively from the time of the Pigul intentions during Shechitah.

7a (Rav Asi): Intent (for Pigul) takes effect on what was lost or burned.

Even though they are not present, intent takes effect on them (as if they are present).

Objection: Rav Asi contradicts what he himself taught!

Question (Rav Asi): Does intent Chutz li'Zemano take effect on Nishpachim (blood that spilled)?

Answer (R. Zeira): You yourself taught that Alal (the hard sinew of the neck) does not join to comprise a k'Zayis for Tum'as Nevelah;

This is because it is unimportant. Likewise, intent should not take effect on Nishpachim, for (proper) Zerikah is not done with them!

Summation of Objection: Above, Rav Ashi said that intent takes effect on what was lost or burned, even though it is unimportant!

Answer (Rava): He means that intent takes effect on what will be lost or burned.

Bava Kama 100a (Beraisa): If the wall between Reuven's vineyard and Shimon's grain field was breached, and Shimon told him to fix it; it was breached, and he told him to fix it, if Reuven decided not to fix it, this forbids the grain, and Reuven is liable.

(Mishnah): If one passes a holed flowerpot through a vineyard, what is growing in the pot is forbidden only if it grew another one part in 200 (while passing through).

Avodah Zarah 73a (Rav Dimi citing R. Yochanan): If one pours Yayin Nesech from a barrel into a pit of wine, even for an entire day, Kama Kama Batel (each bit poured in becomes Batel. It is all permitted.)

Bechoros 22a (Reish Lakish): If one buys brine from an Am ha'Aretz (it is Safek Tamei), Hashakah (connecting it to a Mikveh) is Metaher it, in any case:

If the majority is water, Hashakah is Metaher water;

If the majority is brine, brine is not Mekabel Tum'ah, and the water is Batel in the majority.

(R. Yirmeyah): However, if he will cook it in a pot (and add water), and altogether there will be more water than brine, this arouses the Tum'ah.

Rav Dimi taught this, and Abaye disagreed. Rav Dimi brought a proof from a Mishnah that Tum'ah is aroused again.

Nedarim 57b (Yishmael of Yama) Question: If an onion was uprooted in Shemitah and planted in the eighth year, and the added growth is more than the bulb (that was planted), what is the law?

Answer (R. Ami): R. Yitzchak taught in the name of R. Yochanan that if onions were tithed and planted, when they grow, one tithes the entire amount.

This shows that the bulb is Batel to the additional growth.

Rejection: Perhaps this is a stringency to say that the bulb is Batel.

Yevamos 82b (Mishnah): If a Mikveh had exactly 40 Sa'im, and a Se'ah (of fruit juice) was put in and a Se'ah was removed, it is Kosher.

(R. Yochanan): (We may add and remove) until a majority.

Terumos 5:8 (Mishnah): If a Se'ah of Terumah fell into 100 of Chulin, (it is Batel. We remove a Se'ah, and treat it like Terumah, so Kohanim will not lose.) If before he was able to remove a Se'ah, another Se'ah fell in, it (the entire mixture) is forbidden;

R. Shimon permits.

Rishonim

Rosh (Chulin 7:37): Min b'Mino forbids up to 60 times (the amount of Isur) before it is known that it became mixed. Even though it does not give taste, Chachamim decreed this due to Min b'Eino Mino. However, after the mixture became known and the Isur was Batel in the majority and was transformed to all Heter, and one may eat all of them even at once, we cannot say that its emissions forbid. We find such a difference between before and after knowledge of the mixture in Terumos 5:8. If a Se'ah of Terumah fell into 100 of Chulin, and before he was able to remove a Se'ah, another Se'ah fell in, the first Tana forbids, and R. Shimon permits. The Yerushalmi says that R. Shimon holds that knowledge is Mekadesh, and Chachamim hold that removing is Mekadesh. I.e. R. Shimon would forbid if the latter fell before he knew about the first. Now that he knew about the first, since it is destined to be removed, it is as if it was removed. This is like he holds in general, that blood that was ready for Zerikah, it is as if Zerikah was done. Rabanan do not hold that what is destined to be removed, it is as if it was removed. Therefore, the two Sa'im join to forbid, as if they fell together. According to R. Shimon, once he knew, it is as if it was removed, and everything is permitted. He did not permit before he knew.

Tosfos (7a DH Chishev): The Ri says that Rav Asi asked about one who intended at the time of Zerikah to collect blood that spilled from the bucket and sprinkle it Chutz li'Zemano. Do we say that the blood is Kosher, for he could gather it and throw it? Or since there is no Mitzvah to gather it, it is destined to be lost?

Rashi (7a DH Amar): Since at the time of Zerikah, when he had intent, they were intact, even though later they were lost or burned, intent helps. Here, the meat totally left before Zerikah, so it is as if it is not around at the time of Zerikah. Zerikah does not help to remove Me'ilah from the meat. "It is destined to be lost or burned" is not a Halachah that they must be lost or burned. Rather, now they were lost or burned, even though they were intact at the time of Zerikah. The end reveals about the beginning, that they were destined to be lost or burned.

Tosfos (7a DH Ela): Rava answered that we do not discuss what already was lost or burned. Rather, it is destined to be lost or burned, e.g. he intended at the time of Kabalah for something that was later lost or burned before Zerikah. E.g. he threw a piece of meat or a piece of Eimurim into a dog's mouth or furnace, and he had intent before it reached there.

Tosfos (Avodah Zarah 73a DH Ki): Rav Dimi taught in the name of R. Yochanan that Yayin Nesech is Batel in Heter. Even if at the end there is more Yayin Nesech than Heter wine, we say Kama Kama Batel. This is difficult, for in Bechoros, Rav Dimi holds that Tum'ah is Chozer v'Ni'ur (revived). He does not say Kama Kama Batel! Also, in Nedarim, R. Yochanan holds that added growth is not Batel to the primary plant. He does not say Kama Kama Batel! We must say that here, R. Yochanan permits only until one part in 60 is Yayin Nesech. If it exceeds this, the Yayin Nesech is Chozer v'Ni'ur. If we would not say so, could a person pour milk slowly into a Heter pot (of meat), intermittently, until the milk can be tasted?! Surely we do not. If so, what is the Chidush that Yayin Nesech is Batel until one part in 60? The Mishnah said that Yayin Nesech forbids b'Mashehu. R. Yochanan teaches that this is only when Heter falls into Yayin Nesech, but not if Yayin Nesech falls into Heter. (Then, the Shi'ur is one part in 60.) Rashi says that Kama Kama Batel permits even when there is more than one part in 60 of Isur. How does he explain the Mishnah (74a), which forbids Yayin Nesech that fell into a pit? That is when it flowed in at once. Here, it was poured in drop by drop, so Kama Kama Batel.

Mordechai (Bava Kama 119): If the wall was breached, and Shimon kept telling Shimon to fix it, this forbids the grain. If one passes a holed flowerpot through a vineyard, it is forbidden if it grew one part in 200. Both of these imply that we do not say Kama Kama Batel, and similarly in many places. However, in Avodah Zarah, R. Yochanan taught that Kama Kama Batel, even the entire day! The Rashbam, Ra'avan and Riva answered that when he knew before more was added, we say Kama Kama Batel. If he did not know in between, the Isur is Chozer v'Ni'ur. If Isur fell into 60 parts of Heter, and it was not known until another piece fell in, it is forbidden unless there is enough Heter to be Mevatel both of them. If he recognized it and knew that there is Heter to be Mevatel it, then even if more Isur fell, we do not require a Shi'ur to be Mevatel both of them. We learn from Terumos. The Tosefta says that if he knew before more fell, it is permitted. R. Yochanan permits Yayin Nesech poured into wine even the entire day. This is when he knew that Yayin Nesech was mixed in, and later forgot and poured again, repeatedly.

Tosfos (82b DH Amar): Our Gemara connotes that regarding the majority, we do not say Kama Kama Batel. Also in Shabbos (65b) Shmuel's father was concerned lest rainwater become the majority over the water in the river that comes from the ground. If eighth year growth became the majority over Shemitah, it is permitted. R. Yochanan said that Yayin Nesech poured into Heter, even the entire day, is Batel. The Ri says that it is Batel only until one part in 60. More cannot be Batel, for it gives taste. Ta'am k'Ikar (if an Isur can be tasted in a mixture, the mixture is forbidden) is mid'Oraisa. Even though there is not one part in 60, if it was poured in at once, it would forbid. Chachamim were more stringent about Yayin Nesech to forbid b'Mashehu. R. Yochanan teaches that we are not stringent when it drips in, and we can say Kama Kama Batel.

Poskim

Rema (YD 99:6): If an Isur became Batel, e.g. there were 60 times as much Heter, and later more of the Isur was added, the first Isur is Chozer v'Ni'ur. This is whether it is Min b'Mino or Min b'Eino Mino, whether it is dry or wet, and whether or not he found out in between (that Isur was mixed in).

Gra (15): In Zevachim 31a, we say that Pigul intent is aroused again. (One opinion disagrees, but for a side reason.) Rav Dimi taught that Tum'ah arouses Tum'ah. Abaye disagreed, but he agrees that Tum'ah arouses Tum'ah in the case of the Mishnah. Regarding Kil'ai ha'Kerem, we do not say Kama Kama Batel, and not when rainwater becomes the majority of a river. We say Chozer v'Ni'ur even to be lenient, e.g. growth of Heter is Mevatel the Ikar, and all the more so to be stringent. We say Chozer v'Ni'ur regarding Terumah. Tosfos says that Kama Kama Batel is only for an Isur of Mashehu, but when there is enough to give taste, it is Chozer v'Ni'ur. Orlah is Ma'aleh (helps to be Mevatel) Orlah, and similarly in other cases, but only when there is not enough to give taste. If there is, it is Chozer v'Ni'ur, for it can be tasted.

Gra (ibid.): The Yerushalmi says that knowledge of the owner permits. It asked whether knowledge of someone else permits, and whether Safek knowledge permits. We must say that it depends on knowledge to resolve Kil'ai ha'Kerem, in which each amount is not Batel, with pouring Yayin Nesech into Heter. In the latter case, we say Kama Kama Batel. We cannot say like Tosfos, that Kama Kama Batel helps only when there are more than 60 (so the Isur cannot be tasted), for the Shi'ur of Kil'ai ha'Kerem is one part in 200! Knowledge does not help when the majority is Isur, like the Tosefta in Terumos regarding Orlah, which allows only until there is a majority. Similarly, taking off (from a mixture into which fell) Terumah helps only until there is a majority of Terumah. Similarly, one may add fruit juice to a Mikveh and remove the same volume, until a majority. For Torah Isurim (except for Terumah) we say Chozer v'Ni'ur even when he knew in between, and for Terumah, even if he removed. The Yerushalmi says so. The same applies to dry or wet mixtures Min b'Eino Mino, for Ta'am k'Ikar is mid'Oraisa. Min b'Mino is Batel is the majority. We require 60 mid'Rabanan. We do not say Chozer v'Ni'ur if he knew in between. Likewise, for anything Batel in a Shi'ur of 100 or 200, we do not say Chozer v'Ni'ur, for it (the Shi'ur) is mid'Rabanan. In Avodah Zarah we say Kama Kama Batel even less than 60, for it is Min b'Mino, and if he knew in between. If he did not know, the Isurim add to forbid in 100, 200, b'Mashehu or 60. The Mordechai said that Kil'ayim is Batel in 200 when he did not know. This is wrong. The simple reading of the Mishnah is when he knew. Growth is different, since it is automatic, so it is as if it happened at once. (Therefore, we do not say Kama Kama Batel.) Therefore, the only case (in which Kil'ai ha'Kerem joins to a Shi'ur) is something growing (in a vineyard). Tosfos (100b DH Omer) says that since it grows constantly, it is as if it is at once.