Gemara

(Rami bar Chama): We learn from the Mishnah (2a; we will explain this below) that one can pick up a (Hefker) Metzi'ah to acquire for another. If not, it would be as if each holds half, and the other half is on the ground!

Rejection (Rava): Really, one cannot acquire a Metzi'ah for another. Here, Migo (since) he can acquire for himself, he can acquire for another.

Support: If Reuven told a Shali'ach 'steal for me', Reuven is exempt, but partners who steal are liable. Migo (since) each can acquire for himself, he can acquire also for his partner.

Rami bar Chama learns from the Seifa of the Mishnah. When they admit, or have witnesses, they divide without swearing. If this refers to a bought object, this is obvious! Rather, it refers to a Metzi'ah (that they picked up together). It teaches that one can pick up an object to acquire for another.

Rava holds that we cannot learn from here. Migo he can acquire for himself, he can acquire for another.

9b (Mishnah #1): If Reuven was riding on an animal and saw a Metzi'ah, and told Shimon 'give it to me', if Shimon took it and said 'I acquired it myself', he acquired it. If he said this after giving it to Reuven, Reuven acquired.

(Ula citing R. Yehoshua ben Levi): In a Mishnah (#2), Tana'im argue about whether Levi can acquire Pe'ah for an Oni (Ploni). The case is, Levi is rich. R. Eliezer holds that Migo (since) if Levi would make his property Hefker, Pe'ah would be fitting for him (to take), even when he is rich, it is fitting for him. Migo he could acquire it for himself, he may acquire it for an Oni. Chachamim hold that he cannot acquire for Ploni, for we may use Migo only once';

In Mishnah #1, Shimon said before picking it up that he picks it up for himself.

10a (Rav Nachman and Rav Chisda): If Shimon picked up a Metzi'ah for Reuven, Reuven does not acquire.

This is like one who seizes property (from a borrower) for a creditor when this harms others (other creditors would have wanted to seize the property). He does not acquire. (Here, others would have wanted to take the Metzi'ah.)

Question (Rava - Beraisa): A worker keeps Metzi'os that he finds. This is only if the employer hired him for a particular job, e.g. 'weed for me today.' If he said 'work for me today', the employer gets it.

Answer (Rav Nachman): A worker is different. His Yad (power of acquisition) is like the Yad of his employer (he acquires for his employer).

(R. Chiya bar Aba citing R. Yochanan): If Shimon picked up a Metzi'ah for Reuven, Reuven acquires.

Question: In the Mishnah, Reuven does not acquire (even if Shimon did not say that he picks it up for himself until later)!

Answer (R. Chiya bar Aba): In the Mishnah, Reuven asked Shimon to give it to him. He never asked him to acquire it for him.

Beitzah 39a (Mishnah): The Techum of (extent to which one may take on Yom Tov) water from a pit for Olei Bavel (people ascending to Yerushalayim for the festival) is like the Techum of the one who drew the water.

(Rav Nachman): If David drew water for Levi, it has the Techum of Levi.

(Rav Sheshes): It has the Techum of David.

39b: They argue about whether Levi acquires when David picks up a Metzi'ah for him.

Rishonim

Rif: If Shimon picked up a Metzi'ah for Reuven, Reuven acquires. In the Mishnah, Reuven asked Shimon to give it to him, not to acquire it for him.

Rambam (Hilchos Gezeilah 17:2): If Reuven was riding on an animal and saw a Metzi'ah, and told Shimon 'give it to me', if Shimon took it, and after giving it to Reuven he said 'I acquired it myself', Reuven acquired it.

Rambam (3): If Shimon picked up a Metzi'ah for Reuven, Reuven acquires, even if Shimon did not say anything. If two pick up a Metzi'ah together, they acquire.

Gra (CM 269:1): According to Tosfos (Beitzah 39b DH Hacha), also Rav Sheshes holds like R. Yochanan. Also, the Halachah always follows R. Yehoshua ben Levi, and he holds like R. Yochanan.

Rosh (1:16): If Shimon picked up a Metzi'ah for Reuven, Reuven acquires. All the more so, if two pick up a Metzi'ah together, they acquire.

Rosh (27): The Gemara connotes that one can acquire a Metzi'ah for another only if one can seize for a creditor when this harms others. However, R. Yochanan holds that one can acquire a Metzi'ah for another, but one cannot seize for a creditor when this harms others! R.Tam answered that regarding a Metzi'ah, Migo (since) he could acquire for himself, he can acquire for others. The Halachah follows R. Yochanan, for Rami bar Chama and Ula hold like him.

Ramban (Bava Basra 53a DH No'al): A Tosefta teaches that if one locked and one fenced, it is not a Chazakah. If both of them locked and fenced, it is a Chazakah. Some explains that if each of two people wanted to acquire the property of a convert (who died without heirs), and one locked and one fenced, neither acquires, for each weakens the other's Chazakah. If both of them locked or fenced together, even though each wanted to acquire by himself, since they made the same Chazakah, one does not Mevatel the other. The same Min (type) does not Mevatel itself. Each acquires half, for each helps the other's Chazakah. If this is correct, one may not rely on the Tosefta, for it is unlike Bava Metzia (8b), in which we say that one riding and one leading acquire. Even though they are different Kinyanim, they do not Mevatel each other. I say that the text should say 'if one locked and one fenced, it is a Chazakah', for each did a complete act that helps. If both of them locked or fenced it is not a Chazakah. This is when each built half a fence. Neither's act helped without the other's. The Sugya about picking up a Metzi'ah for another supports this.

Poskim

Shulchan Aruch (CM 269:1): If Shimon picked up a Metzi'ah for Reuven, Reuven acquires. He acquires even if he did not say anything.

SMA (1): This means that if Shimon said that he picks it up for Reuven, Reuven acquires, even if Reuven did not say anything.

Rebuttal (Shach 1): It is even if Shimon did not say anything, just he admits that he picked it up for Reuven. The Poskim connote like this.

Beis Yosef (DH u'Mah she'Chosav Afilu): The Rambam says that Reuven acquires, even if he did not request this. The Gemara connotes like this.

Chidushei Hagahos (in Tur, 1): He refers to 8a, in which we say that two who picked up a Metzi'ah together acquired. Surely they did not say that they acquire for one another, for each says that he acquired it alone!

R. Akiva Eiger: The Ran (Nedarim 34b DH Omar) says that if a Metzi'ah fell within four Amos of a person, and he said that Ploni should acquire it, Ploni acquires it.

Shulchan Aruch (2): If two pick up a Metzi'ah together, they acquire.

Gra (3): Even Rava agrees in this case.

SMA (2): This is whether they picked it up at the same time, or if one picked up one end, and later the other picked up the other end.

SMA (3): One acquires by himself only what is in his hand, since he does not lift the entire object. We assume that each consents to be a Shali'ach for the other, in order that each will acquire half. Therefore, it is as if each totally lifted it, and they are partners in it.

Shulchan Aruch (6): If Reuven was riding on an animal and saw a Metzi'ah, and told Shimon 'acquire it for me', once Shimon picks it up, Reuven acquires, even before it gets to his hand.

SMA (8): This is when Shimon picked it up Stam (without specifying for whom he takes it). If Reuven did not request, Shimon must say that he acquires for Reuven. If not, he can retract.

Rebuttal (Shach 3): Even if Reuven did not request, and Shimon did not say anything, if he intended to acquire for Reuven, he cannot retract.

Rema: Shimon is not believed to say that he acquired it for himself even while it is in his hand.

SMA (9): If Reuven did not request this, and Shimon himself said (afterwards) 'I will picked it up for Reuven', if later he says that he was joking or did not want people to think that he is wealthy, he is believed. Also the Tur says so.

Shach (3): It is unreasonable to believe that he was joking. The Tur does not mention this. The SMA was forced to say this, for he explains that Shimon verbalized his intent.

Nesivos ha'Mishpat (Urim 5): If Reuven did not request this, there is no rationale to say that Shimon was joking! Surely, there is a printing mistake in the SMA. It should say that Shimon said beforehand that he picked it up for Reuven. Therefore, he needs to explain that he was joking.