Gemara

(Rav Yosef): Nowadays, women do not bake more than three Lugim at a time.

Objection (Abaye): This causes a leniency. It exempts the dough from Chalah!

Answer (Rav Yosef): They do like R. Eliezer:

(Mishnah - R. Eliezer): If one removed loaves from an oven and put them in a basket, the basket makes them join [to the Shi'ur for Chalah].

(Rav Yehudah): The Halachah follows R. Eliezer.

Question: R. Yehoshua ben Levi taught that this is only for loaves of Bavel that stick to each other in the oven, but not for long thin loaves!

Answer: R. Chanina taught that it applies even to long thin loaves. (Rav Yosef holds like him.)

Question (R. Yirmeyah): Does a board without a rim join [loaves] for Chalah?

If a Kli with an interior is required, it does not;

Or, perhaps we only require the loaves to be in the airspace of (i.e. above) a Kli!

This question is not resolved.

(Beraisa - R. Eliezer): A basket joins [loaves for Chalah].

R. Yehoshua says, the oven joins them.

R. Shimon ben Gamliel says, loaves of Bavel that stick to each other join.

Chalah (Mishnah 4:1): If each of two women made a dough of one Kav, and they touched, even if they are Min b'Mino, they are exempt. If both belong to one woman, they are obligated only if they are Min b'Mino.

Rishonim

Rambam (Hilchos Bikurim 6:16): If one made a dough less than the Shi'ur, baked it and put it in a basket, then baked another loaf and put it in the basket, if there is a Shi'ur for Chalah gathered in the basket, the basket joins them for Chalah. He separates Chalah from the bread. "B'Achalchem mi'Lechem ha'Aretz" teaches that one separates from what was baked. The oven does not join for Chalah.

Rambam (17): If the loaves bite each other, and one gathered in all a Shi'ur for Chalah, they are obligated, even if they are not in a basket. If one baked a little at a time, and gathered everything on a board without an interior, it is a Safek. For Chalah mid'Rabanan, one need not separate until he gathers them in a Kli with an interior.

Beis Yosef (DH v'Im): The Rambam says so because the Gemara never resolved the question about a board without a brim.

Rosh (Hilchos Chalah 5): Even if there are not five Reva'im in one loaf, the oven joins them. We could have said that the flour in each loaf is Batel in the majority of the loaf, and the oven does not join them. However, the Tosefta connotes that they join. It says that if a Kohen or woman left over flour, the Keren (flour) and Se'or join with it to five Reva'im to forbid the dough. This must discuss flour used to arrange the loaves, for [Stam] flour is exempt. I.e. even though it was Batel, it joins towards five Reva'im to forbid. Even though this Chalah was not surrounded [in a Kli] with the flour mixed in the dough afterwards, since the primary dough was surrounded, this suffices.

Tosfos (48b DH Lo): In Chalah (4:2), the first Tana says that they join only if they bite, and R. Eliezer says "even one who removes from the oven..."! This shows that he does not require that they bite! If the text does not say even, we can say that R. Eliezer requires both.

Terumas ha'Deshen (189): Perush ha'Mishnayos says that biting is when they cling so much that when they separate, one detaches a little of the other.

Poskim

Shulchan Aruch (YD 325:1): If each of two doughs does not have a Shi'ur, if they touch each other until they stick a little to each other, they join.

Shach (1): They join only if one person owns them, like in the next Siman.

Gra (1): This is like the first Tana. R. Eliezer does not argue with him. He merely adds, like he says "even..."

Shulchan Aruch (ibid.): If they do not stick, if they are in one basket, the basket joins them even after they were baked.

Beis Yosef (DH Shtei): The Meforshim [on the Mishnah] explain that "touching" means that they bite from each other, or a basket joins them.

Beis Yosef (DH u'Mah she'Chasav v'Im): Semag and the Ri connote that joining in a basket helps only if they touch each other.

Beis Yosef (DH Kasav): The Rashba says that the Rambam explains that "unless they touch" in the Mishnah is even after they were baked. We require a Kli to join them only when they do not bite each other.

Bedek ha'Bayis: I do not understand what is biting after they were baked. Also, what is his source that the Rambam holds like this?

Beis Yosef (DH Tanya): The Rambam understands that we rule like R. Eliezer, and this also teaches that the Halachah does not follow Yehoshua. The Rosh connotes [like R. Yehoshua] that the oven join them. The Rashba says "one could have explained that R. Yehoshua means that the oven join them but a basket does not, and R. Eliezer means that even a basket joins. However, the Yerushalmi brings a Beraisa that says that a basket joins but an oven does not, and a Beraisa that says vice-versa. If so, presumably for Chalah of Eretz Yisrael, which is mid'Oraisa, both of them join, and one is liable due to Safek. In Chutz la'Aretz, only a basket joins, like R. Eliezer. The Rambam did not distinguish between Eretz Yisrael and Chutz la'Aretz. I do not know why."

Beis Yosef (ibid.): Perhaps the Rambam explains that the Tana'im who argue in the Yerushalmi are R. Eliezer and R. Yehoshua. The Halachah follows R. Eliezer, that only a basket joins. Perhaps the Rambam holds like the Rashba, but he did not distinguish between Eretz Yisrael and Chutz la'Aretz because nowadays Chalah is only mid'Rabanan even in Eretz Yisrael, like he wrote in 5:5.

Gra (3): In the Yerushalmi, R. Yochanan says that in both cases they bit. This is unlike the Bavli. We hold like Rav Yosef and Abaye. Tosfos [deletes "even" from the text] and R. Shimshon [says that if the text says even, it means that R. Eliezer both require biting, and R. Eliezer holds that it can even be after baking]. If so, also R. Chanina [holds like this]. However, we cannot say that the Amora'im argue about the text! Rather, he holds that the basket joins them, but biting does not. The Rambam, Tur and other Poskim rule also like the first Tana. R. Eliezer discusses biting in the basket. The first Tana holds that biting must be while they are dough. R. Chanina does not require biting at all. He does require touching even in the basket according to R. Eliezer. Semag and the Rosh say so. In 2:4, it says that they touched. This is like R. Eliezer, who does not require biting.

Gra (3): The Rambam rules that an oven does not join. The Gemara did not say that the Halachah follows also R. Yehoshua. This is primary. In the Yerushalmi, R. Yochanan means that R. Eliezer and R. Yehoshua argue only when they bit. We hold like R. Eliezer, so an oven does not join even if they bit.

Shulchan Aruch (ibid.): If they were put on a board without a rim, they do not join.

Shach (2): The question was not resolved. The Mechaber is lenient, because nowadays Chalah is mid'Rabanan.

Rema: Therefore, when we join them in a Kli, one must be careful that nothing be totally above the walls of the Kli. I.e. no loaf or dough may be totally above the walls.

Beis Yosef (DH u'Mah she'Chasav Lachen): This follows from the unresolved question about a board without a brim. I.e. the entire loaf or dough may not be totally above the walls of the Kli. If part is in the Kli, even if part is above the walls, it joins. Semag connotes that according to the Ri, even if the entire loaf or Matzah is above the walls of the Kli, they join. He wrote that when putting the Matzos in the Kli, all must be within the walls, for we asked about a board without a brim [and did not resolve it]. However, the Ri says that the question is only if it has no brim. If it has a brim, even if [the loaves or doughs are] piled up above it, they join. This is because it is like the airspace of a house, which joins, like it says in Eruvin in the Yerushalmi.

Taz (2): The Tur wrote only that nothing may leave above the walls of the Kli. The Beis Yosef and Rema explained [that a loaf may not be totally above]. The Tur connotes that it may not be even partially above! However, the Beis Yosef and Rema are correct. If even part is a problem, why does it not join when the loaf is below in the air of the Kli, just like doughs that bite each other, which are only slightly connected, and even so [they join as if they were totally] connected?!

Shach (4): If part is inside, it joins, for this is unlike a board [without a brim].

Gra (7): This is like the Beis Yosef, He is correct. A basket joins like doughs that bite. It suffices for a little to bite.

Rema (ibid.): Some say that if he covers them with a cloth, this is considered like a Kli to join them.

Shach (5): Why does the Rema say "some say"? No one argues! Also the Tur wrote this Stam. Also the Maharil says that this works.