Gemara

(Mishnah): A Keli is Metzaref (joins) its contents for Kodesh it (if there are pieces of Kodesh inside, if Tum'ah touches one of them it is as if it touched all of them, even if they do not touch each other), but not for Terumah.

(R. Chanin): We learn from "Kaf Achas" that everything in the bowl (of Ketores) is considered like one.

Question (Rav Kahana): A Mishnah shows that this is only mid'Rabanan!

(Mishnah): R. Akiva further testified that if a Tevul Yom touched part of the Soles (fine flour of a Minchah), Ketores (incense), Levonah (frankincense) or coals, he was Posel all of it.

Question: How do we know that this is only mid'Rabanan?

Answer: In the Reisha, R. Shimon ben Beseira testified that if a Tamei person touched some Efer Chatas (ashes of Parah Adumah), he was Metamei all of it. R. Akiva further testified, i.e. also his testimony was mid'Rabanan.

Answer (Reish Lakish): R. Akiva testified about Shirayim of a Minchah (what remains after Kemitzah). Mid'Oraisa, a Keli is Metzaref Kodesh that needs (to be in) a Keli. Chachamim decreed Tziruf even when it does not need a Keli.

Question: This answers for Soles. How can we answer for Ketores and Levonah? (They always need to be in a Keli!)

Answer (Rav Nachman): The case is, they were gathered on a (flat) cooked hide. Mid'Oraisa, only a Keli with an interior is Metzaref Kodesh. Chachamim decreed that even a Keli with no interior is Metzaref.

He (R. Chanin) argues with R. Chiya bar Aba:

(R. Chiya bar Aba citing R. Yochanan): The Mishnah (that teaches about Tziruf for Kodesh) is derived from R. Akiva's testimony:

Menachos 24a - Question (R. Chiya): (If a Minchah is in a Keli in two parts that do not touch each other,) may one take Kemitzah from one of the parts? (Is this like taking from the entire Minchah?)

If Tziruf Keli is mid'Oraisa, it applies even when this is a leniency;

If Tziruf is mid'Rabanan, it is only to be stringent.

Taharos 1:9 (Mishnah): If Hekdesh loaves and (Rambam; R. Shimshon - or) Kodesh water are in their cavities, if a Sheretz touched one of them, they are all Temei'im. Regarding Terumah all are Temei'im only if they are connected by liquid Tofe'ach (enough to wet something).

Rishonim

Rashi (Pesachim 19a DH Alma): We know that R. Akiva holds that Tziruf is only mid'Rabanan because he learns from Levonah and coals. (They are not foods, so) their Tum'ah is only mid'Rabanan.

Rebuttal (Tosfos Chagigah 23b DH v'Ha): Also their Tum'ah is mid'Oraisa! Rather, R. Akiva adds to the law taught previously of Tziruf of ashes of Parah Adumah. Their Tum'ah is mid'Rabanan.

Rambam (Hilchos Avos ha'Tum'ah 12:7): A Keli is Metzaref its contents for Kodesh, but not for Terumah. If a Keli was full of distinct fruits, such as raisins or dried figs, and Tum'ah touched one of them it is as if it touched all of them, the entire Keli becomes Tamei for Kodesh, but not for Terumah. This and all the stringencies of Kodesh over Terumah are mid'Rabanan. This stringency has a hint in the Torah - "Kaf Achas", everything in the bowl is considered like one. Even a Keli without an interior is Metzaref what is on it for Kodesh, e.g. if pieces of Kodesh were on a tablet or hide, even if they do not touch each other.

Kesef Mishneh: R. Chanin holds that Tziruf for Kodesh is mid'Oraisa. The Rambam rules like R. Yochanan, that it is mid'Rabanan, because R. Yochanan is cited in the Gemara more regularly than R. Chanin.

Question: Tziruf is only for Kodesh. Figs are not Kodesh!

Answer #1 (Griz Menachos 24a DH Hoshit): Perhaps the Rambam refers to figs with Kedushas Damim, and this is enough for Tziruf.

Pri Etz Chayim (Bikurim Siman 38): In some ways Bikurim are unlike Kodshim, e.g. a Mechusar Kipurim may eat it. In some ways they are like Kodshim, e.g. Me'ilah applies to them. Tana'im (Makos 18b) argue about after the Kohen gets them, whether they are like Kodshim received from Shulchan Gavoha, or if they are Matanos Kehunah like Terumah (that had Dinei Kodshim as long as they were needed for Avodah).

Note: This gives a second answer, that the Rambam discusses Bikurim.

Rambam (Hilchos Parah Adumah 13:5): If a Tamei touched some Efer Chatas, he was Metamei all of it.

Perush ha'Mishnayos (Idiyos 8:1): Touching some Efer Chatas makes all of it Tamei due to Tziruf Keli. The Halachah follows R. Akiva, who applies Tziruf Keli even when it has no interior.

Rambam (Hilchos Tum'as Ochlim 8:9): If a Tevul Yom touched part of the Soles, Ketores, Levonah or coals, he was Posel all of it. This refers to coals scooped (from the Mizbe'ach) with the pan on Yom Kipur, for in the same pan they are brought into the Heichal. However, on other days they are poured from a silver pan into a gold pan. If they fall on the floor they have no Kedushah; they are swept to the Amah (a small stream going through the Azarah).

Rebuttal (Ra'avad): Indeed, the Yerushalmi (Chagigah 3:2) says so, but it concludes that since they already needed to be in a Keli (from when they were scooped), if a Tevul Yom touched some of them he was Posel all of them.

Defense (Kesef Mishneh): The Rambam explains that the latter opinion in the Yerushalmi is not the conclusion. It is an argument. Since it is mid'Rabanan, the Rambam follows the lenient opinion.

Tosfos (Yoma 46b DH Ki): R. Nisim Ga'on explains that the Yerushalmi asked why Tziruf helps for coals. The coals that fall on the floor are swept to the Amah, i.e. they have no Kedushah! It answers that Tziruf applies on Yom Kipur, when they need to be in the Keli; they are brought in to the Heichal in the same pan. R. Baruch says that the Yerushalmi asks, since not all of the coals are needed, why does Tziruf apply? It answers that Tziruf applies on Yom Kipur, when all of the coals are needed. Alternatively, it could have answered that Tziruf applies on every day in the gold pan, for all the coals in it are needed. The Gemara (Chagigah 24a) says that mid'Rabanan, Kelim are Metzaref even what is not needed. This is only according to the opinion that Tziruf is mid'Oraisa (but the Yerushalmi holds that it is mid'Rabanan).

Tosfos Yeshanim (Yoma 45a Sof DH Nispazru): The opinion that Tziruf is mid'Rabanan could say that Kelim are Metzaref only what is needed.

Ri (in Tosfos Chagigah 23b DH she'Im, according to Ra'avad Tamid 5:5): Tziruf always applies, even in a Chol Keli.

Note: The Maharsha says that the Ri holds that a Chol Keli is not Metzaref.

Ra'avad (Tamid 5:5): Perhaps R. Masniya in the Yerushalmi holds that R. Akiva's Chidush was that Tziruf Keli helps even for things that are not foods.

Rambam (Hilchos Pesulei ha'Mukdashim 11:23): If a Minchah was divided in a Keli in two parts that do not touch each other, it is a Safek whether or not the Keli joins them to permit taking Kemitzah from one part. Therefore, one should not do so. If he did, he should not burn the Kometz on the Mizbe'ach. If he did, the Minchah is accepted, but the Shirayim are not eaten.

Question (Chak Nosan Menachos 24a Mahu): The Gemara said that Tziruf helps for Kemitzah only if Tziruf (for Tum'ah) is mid'Oraisa. Since the Rambam rules in Hilchos Avos ha'Tum'ah (12:7) that Tziruf is mid'Rabanan, he should say that Vadai it does not help for Kemitzah! Here, in Halachah 27, the Rambam discusses a Minchah in which half was lost, more was Hukdash in its place, and the lost half was found. He rules that Tziruf (Vadai) helps for Kemitzah! Indeed, Rava said so. However, perhaps Rava teaches that if Tziruf is mid'Oraisa, it helps for Kemitzah, but he himself is unsure whether or not it is mid'Oraisa. And even if Rava was sure, since the Rambam rules like Rav Kahana who was unsure, he should rule similarly in Rava's case! Also, in Hilchos Avos ha'Tum'ah (12:7) the Rambam rules that even a Keli without an interior is Metzaref. The Gemara said this only to answer for the opinion that Tziruf is mid'Oraisa! We can answer the first question by saying that the Rambam's text did not say that Tziruf for Kemitzah depends on Tziruf for Tum'ah. However, the other questions are difficult.

Perush ha'Mishnayos (Taharos 1:9): Even if Hekdesh loaves touch each other where they are dry, we consider that the water in the cavity touches the next loaf due to Chibas ha'Kodesh. The water is always a Rishon l'Tum'ah, so every loaf becomes a Sheni.

R. Shimshon (1:9): All the Hekdesh loaves are Temei'im due to Tziruf Keli. Mid'Rabanan this applies even if the Keli has no interior and the Hekdesh does not need the Keli.

Tosfos (Yoma 48b DH mid'Pasil): Chachamim decreed that a Keli with no interior is Metzaref like a Keli with an interior, but no more. I.e., it is Metzaref only Kodesh that needs the Keli.

Question (Tosfos Menachos 24a DH she'Ein): Here, Rav Kahana is sure that a Keli is Metzaref only what needs the Keli. In Chagigah we say that this is mid'Oraisa, but mid'Rabanan it is Metzaref even what does not need the Keli!

Answer #1 (Tosfos): Perhaps Rav Kahana holds like Rabah bar Avuha, who says that Chachamim decreed only that a Keli with no interior is Metzaref.

Question (Turei Even Chagigah 24a DH mid'Oraisa): Also there the Kodesh does not need the Keli, for such a Keli is not Mekadesh (so it is still difficult for Rav Kahana)!

Answer #2 (Tosfos): Rav Kahana holds that Tziruf applies (mid'Rabanan) to Kodesh that previously needed a Keli.

Answer #3 (Turei Even): According to the opinion that Tziruf is mid'Rabanan, it applies only to what needs the Keli. It is difficult why the Rambam (Tum'as Oclhim 12:7) says that Tziruf applies to raisins or dried figs. They do not need a Keli!

Question (Emek ha'Netziv Nasa p.182): Why do we expound "Kaf Achas", instead of "Ka'aras Kesef Achas" or "Mizrak Echad", which come earlier? Especially according to Reish Lakish, who says that Tziruf Keli is mid'Oraisa and applies even to be lenient to Metzaref a Minchah, we should learn from these (they were filled with Soles for a Minchah)!

Answer (Emek ha'Netziv): Had we expounded one of them, one might have thought that Tziruf Keli is only when the Keli must Mekadesh the Kodesh.

Merumei Sadeh (Chagigah 23b DH veha'Ikar): Kodesh does not need the Keli if it must be removed, e.g. an extra half Isaron, or Shirei Menachos that must be given to a Kohen. Produce that is difficult to carry by hand needs a Keli.