Gemara

31b (Mishnah): If Peros fell into an irrigation channel, and Reuven's hands were Tamei and he stuck his hands in and removed the Peros, his hands become Tehorim and the Peros are not Huchshar.

If he wanted to wash his hands, his hands become Tehorim and the Peros are Huchshar.

36b: "(Kodesh) meat that will touch anything Tamei (may not be eaten)" teaches that meat of Korbanos becomes Huchshar (able to receive Tum'ah).

Question: How was the meat Huchshar?

i. R. Chiya bar Aba taught that blood of Kodshim is not Machshir. R. Yosi b'Ribi Chanina taught that liquids of the Mitbach (the place in the Mikdash where the meat is rinsed) are not Machshir!

Answer: The meat is Huchshar through Chibas ha'Kodesh (a stringency of Kodshim).

Rejection: Perhaps the Hechsher was (not through Chibas ha'Kodesh, rather,) like Rav Yehudah established;

(Rav Yehudah): A Shelamim was taken through a river, and it was still wet when it was slaughtered.

Bava Kama 12b (Beraisa - R. Yosi ha'Glili): "He transgressed in Hash-m (and denied his fellowman)" includes Kodshim Kalim, which (pertain to Hash-m and) are (also) Mamon Ba'alim (the owner's property).

(Mishnah): If one was Mekadesh with his portion of Kodshim, whether Kodshei Kodoshim or Kodshim Kalim, the Kidushin is invalid (for one does not own his portion).

This can even be like R. Yosi ha'Glili. He said that Kodshim Kalim are Mamon Ba'alim only in the life of the animal. After Shechitah, he agrees that they are considered Hash-m's, just one may eat them.

Question: Does R. Yosi ha'Glili really hold that Kodshim Kalim are Mamon Ba'alim in the life of the animal?!

(Mishnah): A Tam (unblemished) Bechor (male firstborn animal) may be sold when alive. If it is blemished, it may be sold alive or slaughtered. He (the Kohen) may use it to be Mekadesh a woman.

(Rav Nachman): This is only nowadays. Since it cannot be offered, Kohanim own it. When the Mikdash stands, Kohanim do not own it.

98a (Beraisa): If Reuven worked with (and thereby disqualified) Shimon's Parah Adumah (red heifer), or with his Mei Chatas (water destined to be sanctified with ashes of a red heifer), he is exempt b'Yedei Adam, but liable b'Yedei Shamayim.

Zevachim 114a - Question: If an animal was Ne'evad or Muktzeh (worshipped or designated for worship), since no action was not done to the animal itself, only the owner can forbid it. Once it is Hekdesh, he ceases to own it!

Answer: Our Mishnah discusses Kodshim Kalim. It is like R. Yosi ha'Galili, who says that Kodshim Kalim are considered Mamon Ba'alim.

Pesachim 19a (Mishnah): If a needle was found in (Kodesh) meat, the meat is Tamei.

Rishonim

Rambam (Hilchos Nizkei Mamon 8:1): If a person's ox gored a Hekdesh ox or vice-versa, it is exempt. Payment of damage does not apply to any Hekdesh to which Me'ilah applies.

Lechem Mishneh: This is like R. Yosi ha'Glili, who holds that there is Hekdesh to which Me'ilah does not apply, i.e. Kodshim Kalim. They are Mamon Ba'alim, so payments for damage apply to them.

Support (Ketzos ha'Choshen 406:1): We say (Chulin 36a) that perhaps a Shelamim was taken through a river, and it was still wet when it was slaughtered, and this was Machshir it. The Rambam (Hilchos Tum'as Ochlim 12:1) says that Hechsher requires the owner's Ratzon (desire) that it become wet. On 114a, the only way we find that someone owns a Korban is Kodshim Kalim, according to R. Yosi. This explains why Rav Yehudah mentioned a Shelamim (it is Kodshim Kalim).

Rambam (Hilchos Tum'as Ochlim 10:16): Since blood of Kodshim is not Machshir Kodshim slaughtered in the Azarah, the meat is Huchshar only through liquids that fall on it, other than liquids of the Mitbach.

Rambam (17): If a Kodshim cow was passed through a river, and it was slaughtered when there was still liquid Tofe'ach (enough to wet what touches it) on it, it is Huchshar.

Rambam (12:1): Any of the seven liquids are Machshir. This is only if it was put on the food with the owner's Ratzon after the liquid was uprooted from the ground.

Rambam (2): Any liquid that fell on food initially with the owner's Ratzon, even if in the end he is displeased, or if initially he was displeased but at the end he was pleased, it is Huchshar.

Ra'avad: Do not say that initially the owner's Ratzon that it fall on the food. Rather, initially he wanted the liquid for any detached use, even if in the end he is displeased that it fell on the food from the beginning. It is Huchshar.

Oneg Yom Tov 32 (DH Shuv): The Rambam agrees. He discusses liquids that were initially attached, so the first Ratzon is needed to make them considered liquids. If a liquid was initially detached, and one wanted it (for something), if later it fell on Peros, it is Machshir even if he was displeased. This is how we find Hechsher regarding Isurei Hana'ah such as Orlah and Kil'ai ha'Kerem, even though no one owns them.

Rashi (36b): Rav Yehudah discussed a Shelamim, because the verse (of Tum'as Basar brought above in the Gemara) discusses a Shelamim. Also, the owner of a Shelamim keeps the skin, so it is common to pass it through a river so the skin will flay nicely.

Rashi (Pesachim 20a DH Hai): The Gemara did not ask how to explain the verse that says that Kodshim meat receives Tum'ah, for this is not difficult. Shelamim may be eaten anywhere in the city. They rinse and cook it, so it is Huchshar. We asked only about an animal in the Azarah, since according to R. Chiya bar Aba, it is not Huchshar.

Ketzos ha'Choshen (DH v'Nicha): According to Rashi, why did the Gemara need to say that one took the cow through the river? Shelamim is eaten in the entire city, so it can be Huchshar outside the Mikdash, when it was rinsed or cooked! Rather, it is because we establish the Mishnah of Kidushin with Kodshei Kodoshim or Kodshim Kalim even like R. Yosi ha'Glili. He agrees that after Shechitah, they are considered Hash-m's. This is why we needed to say that it was Huchshar when it was alive. After Shechitah it is not the owner's, so there is not Ratzon of the owner. Even though Hechsher does not take effect until after Shechitah, it is still the owner's until after the four Avodos are finished.

Rashba (31b DH Peros): Tosfos derived from here that Hechsher does not require the owner's Ratzon. 'One whose hands were Tamei' connotes even if he is not the owner. Also, we learn from "Ki Yutan", which connotes whether the owner or someone else willingly put, like we say about Eglah Arufah (Pesachim 26b) and Parah Adumah (Sotah 46a). One who does Melachah with Mei Chatas or a Parah Adumah is liable b'Yedei Shamayim. This disqualifies, even though the owner does not want it. However, the Rambam (Hilchos Tum'as Ochlim, Perek 12) requires the owner's Ratzon.

Kesav Sofer (CM 28): The Chasam Sofer (YD 39) agreed with the Ketzos ha'Choshen. Tosfos (Bava Kama 98a DH Ha) distinguishes. If a Melachah happens by itself, then we require that the owner is pleased. If one does the Melachah, it suffices that that person wants it. We can say that the Rambam requires the owner's Ratzon only when the water came by itself, but not if one put water on it. Rav Yehudah discusses such a case,. i.e. passing it through a river. The Rashba challenged the Rambam from Parah Adumah and Mei Chatas. The questioner derived that he holds unlike Tosfos, and requires the owner's Ratzon even when another acts on it. I say that the Rashba says so only regarding a Parah Adumah that entered to nurse and thresh. One is exempt because he did not do anything. He merely was pleased. If he worked with it, the Rashba agrees that the Rambam does not require the owner's Ratzon. This is unlike the Ketzos ha'Choshen (who requires the owner's Ratzon for Hechsher, even though he overtly wets it). However, perhaps the Ketzos ha'Choshen holds like Rashi (Pesachim 20a DH v'Adayin), who says that (if the skin was still wet), it is impossible that no water will fall on the meat during flaying. It is considered to happen by itself, so we can require the owner's Ratzon.

Oneg Yom Tov (32 DH uv'Zeh): Rashi said that the Gemara asked only about the Mishnah, but not regarding the verse, for the verse discusses meat that is eaten in the entire city, and it is easily Huchshar. The Ketzos ha'Choshen challenged this, for Rashi holds that after Shechitah it does not belong to the owner any more! I answer that if a liquid was initially l'Ratzon, it is Machshir even if later it falls on the food without the owner's Ratzon, like Rashi (Chulin 16a DH l'Inyan) and the Rambam (Hilchos Tum'as Ochlim 10:16,17) say. The Rambam holds that there is Hechsher outside the Azarah. According to the Ketzos ha'Choshen, this is impossible, for it has no owner! Rather, if the liquids were initially l'Ratzon, we do not require Ratzon when they fall on the food. In Chulin, we sought a source for Chibas ha'Kodesh. Reish Lakish understood that the verse teaches that any Kodshim is Mekabel Tum'ah, including Chatas, which never leaves the Azarah. Also, there is an opinion that the Se'ir Chatas (on the day of Chanukas ha'Mishkan) was burned due to Tum'ah. We reject the proof; perhaps the animal was passed through a river.

Rosh (Bechoros 5:1): A Mishnah teaches that one may sell a Bechor Tam when alive, and blemished alive or slaughtered. He may use it to be Mekadesh a woman. Rav Nachman said that this is nowadays, when it cannot be offered, so Kohanim own it.

Poskim

Shulchan Aruch (YD 306:6): Nowadays, a Kohen may sell a Bechor even to a Yisrael when it is Tam (unblemished) and alive, or when it has a Mum alive or slaughtered. He can be Mekadesh a woman with it, for it is like any of his property.

Shulchan Aruch (EH 28:23): Nowadays, if the owner of a Bechor was Mekadesh a woman with it, she is Safek Mekudeshes.