Gemara

34b (Rav Nachman): If two each claim 'I inherited this land (or ship) from my fathers', Kol d'Alim Gevar (whoever overpowers takes it).

Question: Why is this different than two documents with the same date (giving the same field to Levi and Yehudah)?

(Rav): Levi and Yehudah split the property.

(Shmuel): The judges use their discretion.

Answer: There, we will never know which document was given first. Here, perhaps one will bring witnesses later. (We do not want to give a ruling that might be overturned later.)

Question: Why is Rav Nachman's case different than the following?

(Mishnah): Levi traded his cow for Shimon's donkey, or sold his slave to Shimon. (The cow or slave was not in front of us at the time.) Later, we see that it gave birth. Levi claims that the birth was before the sale (so the child was not sold). Shimon claims that it was after, and he acquired a pregnant mother, so the child is his. They divide the value of the child.

Answer: There, each has Drara (grounds to suspect that it is his; Alternatively, Beis Din would have a doubt even without their claims) of money.

Bava Metzia 100a - Question: Why do they divide? The one in whose premises the baby lies is Muchzak. The other must bring proof to receive!

Answer (R. Chiya bar Avin): The case is, the calf is in the swamp, and the slave is at the selling-block (neither owns the premises).

Question: The seller is Muchzak. The buyer must bring proof to take from him!

Answer: The Mishnah is Sumchus, who says that when we are in doubt, we divide the money without an oath.

2a (Mishnah): Reuven and Shimon are holding a garment. Reuven says 'I found it', and so does Shimon; Reuven says 'it is mine', and so does Shimon. Each swears that he does not own less than half, and they divide it.

3a - Suggestion: Our Mishnah is not like R. Yosi:

(Beraisa - R. Yosi): (Reuven and Shimon deposited money with by Levi, who forgot who gave which amount; each claims the larger amount.) We make the liar lose (to induce him to admit). Neither side gets anything until Eliyahu comes and resolves the matter (or one side admits).

Question: The Mishnah is also unlike Chachamim! (They say that each side gets the smaller amount, but) they agree that we leave what is contested (the rest) until Eliyahu comes. Here, the entire garment is contested!

Answer: The Mishnah can be like Chachamim. There, all the contested money belongs to one of them, so we leave it (until Eliyahu comes). Here, perhaps each owns half, so they swear and divide it.

However, R. Yosi says that we leave even the smaller amount, which surely each side is entitled to. Here, perhaps one side is not entitled to anything, all the more so he would say that we leave it!

Rejection: Our Mishnah can be like R. Yosi. He discusses when one party is surely lying. Here, perhaps neither intends to lie. Perhaps they picked it up at the same time (and each thinks that he picked it up first)!

Rishonim

Rambam (Hilchos To'en 9:7): If two were holding one Kli, or they are sitting near a stack of wheat in a Simta (shoulder of Reshus ha'Rabim) or joint Chatzer, and each says 'it is mine', each swears while holding a (Kodesh) Chefetz (e.g. Sefer Torah or Tefilin) that he does not own less than half, and they divide it. The oath is a Rabbinical enactment, lest one grab another's garment and receive (half) without swearing.

Rosh (Bava Metzia 1:1): Since both of them are Muchzak in the Talis, we must rule that they divide it. We consider anything we see in a person's hand to be his, even if another claims 'it is mine.' If one was holding something and another grabbed it, even though he says that he grabbed his own, we say that it belongs to the one who was holding it (Bava Basra 33b). Therefore, we cannot rule that Kol d'Alim Gevar (whoever overpowers will take it), like we say about a contested boat (Bava Basra 34b). There, neither is Muchzak, so Beis Din need not protest if one seeks to take something that he claims is his, and we do not know whose it is. Therefore, we do not rule that they divide it, lest we improperly make one of them lose (half). It is better to say that whoever overpowers with force or proofs will take it. It is likely that the owner will be able to bring better proofs, and will strive harder to keep his own property. The other will not try so hard, for he fears lest his opponent will later bring a proof and take it away. Here, each is Muchzak. If we would say Kol d'Alim Gevar, one would steal from the other's hand. This is not only regarding a Metzi'ah or sale in which both paid, in which it could belong to both of them. Rather, even in a sale in which only one paid, or if each claims that he wove it, and clearly one of them is lying, they divide it. We learn from the case of two holding onto a document (Bava Metzia 7a). Even though surely one lies, they divide it. Chachamim (of R. Yosi) hold that we divide with an oath whenever the division could be true, even if there is a definite Ramai. The rule is, if both are Muchzak, we divide with an oath. If neither is Muchzak, Kol d'Alim Gevar. If one is Muchzak, we do not take it from him. The only exception is different deposits. It is as if both of them are Muchzak, for the Shomer holds for both of them, but we leave the money (that the larger exceeds the smaller), for the Shomer knew from the beginning that this money does not belong to both of them.

Poskim

Shulchan Aruch (CM 138:1): If two were holding one Kli, or they are sitting near a stack of wheat in a Simta or joint Chatzer, and each says 'it is mine', each swears (while holding a Chefetz) that he owns part, and he does not own less than half, and they divide it.

SMA (1, citing the Tur): Since the stack is in a place where they could acquire, and they are next to it, it is as if they are Muchzakim in it.

Shach (1): This is only if both of them are near the stack. If not, it is not as if they are Muchzakim in it. In Bava Basra, we asked why the argument about the boat is unlike the sale of the pregnant cow or slave, and it is clear from Bava Metzia 100a that the latter is in a Simta or swamp.

Gra (2): We learn from a Talis. Even if they merely hold the fringes (which is unlike having a true hold on the item), they divide it

Rema: However, if one owns the house, and brought the other in to live with him, and they argue about property in the house, it is in the Chazakah of the one Muchzak in the house.

SMA (4): This refers to property in the house. If they argue about something Hefker that entered the house, they are equal in it.

Shach (2): This is even if the one Muchzak does not own the house, rather, he rents it. If both pay rent, they divide what they argue about.

SMA (6): The Tur says that Rashi holds that they divide only when it is possible that both acquired together. However, if each claims 'I wove it', we leave it until Eliyahu comes. The Shulchan Aruch did not distinguish. This is like the Ri and Rosh, who say that also in this case, we divide it. see Sha'ar Mishpat 1 to explain Gra (Sedei Eliyahu?

Shulchan Aruch (ibid): If one tells the other 'swear and take the entire item', we heed him. If also the other does not want to swear, they divide without an oath.

Gra (6): If an enactment was made to benefit a person, he can say 'I do not want the enactment.'

Shach (3): Since Reuven must swear, Shimon can make him swear through Gilgul (once one must swear, his opponent can make him swear about other matters) that he owns the entire object (since Reuven will receive it all).