Gemara

85a (Beraisa): If goods were deposited with Dan, the buyer does not acquire until Dan allows him to use the premises to acquire, or rents the premises to him.

144a (Mar Zutra): Chachamim made three enactments without reason (how they work). One of them is Ma'amad Sheloshtan:

(Rav): If Reuven says to Shimon 'you have money of mine. Give it to Levi', and all three are present, Levi acquires the money.

149a: Isur had deposited money with Rava. Isur was about to die, and wanted to give the money to his son Rav Mari, who was away. Isur had converted after the conception of Mari. (Mari would not inherit Isur. Isur had no heirs.)

Rava: Isur has no way to give the money to Mari! ... If he wants to give through Ma'amad Sheloshtan, I will not go.

(Rav Ika brei d'Rav Ami): Isur can admit that the money belongs to Rav Mari. Rav Mari will acquire through Odisa (Kinyan through (even a false) admission)!

Gitin 13b (Rava): Presumably, Rav's law applies only to a deposit (Shimon could give it over), but not to a loan. However, Rav actually said it even about a loan!

(Shmuel): If Reuven says to Shimon 'you borrowed money from me. Give it to Levi', and all three are present, Shimon owes the money to Levi.

Question: Why does this work?

Answer #1 (Ameimar): It is as if Shimon said when he borrowed the money 'I am indebted to you, or anyone who will come in your stead.'

Objection (Rav Ashi): If so, one could not give the loan to one born after the loan was given! All require the recipient of an acquisition to be in the world!

Answer #2 (Rav Ashi): Rather, through the benefit of converting an old loan into a new loan, Shimon is able to obligate himself to Levi.

Objection (Huna, son of Rav Nechemyah): If so, Rav's law would not apply if Levi is the type who forces people to pay immediately! (Shimon does not prefer to owe such a person. Surely, the law does not depend on the recipient!)

Answer #3 (Mar Zutra): Rav's law is an enactment without reason (how it works).

Rishonim

Rosh (Gitin 1:17): The Riva says that Ma'amad Sheloshtan works b'Al Korcho (against the will) of Shimon (the borrower). If it required his consent, why did Chachamim need to enact Ma'amad Sheloshtan for a deposit? Ten k'Zechi (saying 'give' is like saying 'acquire for')! If goods were deposited with Dan, once Dan agrees, the buyer acquires them (Bava Basra 85a). Rather, Ma'amad Sheloshtan is needed when Shimon does not consent.

Question: R. Tam holds that Ten k'Zechi only when the object is given over, and it does not apply to gifts. Perhaps Ma'amad Sheloshtan does not work b'Al Korcho. It is needed for gifts, or when the object is not given over!

Answer (Tosfos 13b DH Gufa): Still, the giver can explicitly say 'Zechi'!

Rebuttal (Ran DH Maneh): Perhaps Ma'amad Sheloshtan does not work b'Al Korcho. It is needed for when the object is not in Shimon's Reshus!

Defense #1 (Tosfos): In any case, Reuven can give it to Levi through Odisa, like it says in Bava Basra 149a.

Defense #2 (Rosh, ibid.): Surely, Chachamim would not make an enactment without reason (how it works) for an unusual case when Shimon does not have the deposit now. (Rather, it is needed to work b'Al Korcho of Shimon.) Another proof is from Rava, who said 'if Isur wants to give through Ma'amad Sheloshtan, I will not go.' This connotes that if he would be there, it would work b'Al Korcho. Rava did not mean that he would be ashamed to refuse, for even without Ma'amad Sheloshtan Isur could ask him to acquire for Rav Mari. It is difficult to say the money was not in Rava's Reshus at the time.

Rebuttal (Ran DH Maneh): It is reasonable that Rava would remove the money from his Reshus, in case Rav Mari will tell him 'Zechi'!

Note: Presumably, the Rosh holds that a Shomer may not remove the deposit from his Reshus. I do not know the Ran's source to disagree.

Rosh and Ran (ibid.): According to the reason that Ma'amad Sheloshtan works with Shimon's Hana'ah that an old loan becomes a new loan, it seems that it requires his consent. Even though that reason applies only to loans, it is unreasonable that Ma'amad Sheloshtan was enacted in two different ways.

Rebuttal (Rosh): Chachamim enacted based on most people, who prefer that an old loan become a new loan. If a particular borrower is unhappy, we ignore his opinion. Rav Ashi said that it is as if Shimon initially indebted himself '...to anyone who will come in your stead.' This does not prove that it is b'Al Korcho. Perhaps it means '... to anyone in your stead to whom I will agree to be indebted.' The Halachah is, it works b'Al Korcho.

Rashba (13b DH Omar): Alternatively, when Shimon agrees, it is considered as if he said from the beginning 'I am indebted...'

Poskim

Shulchan Aruch (126:7): If Shimon had Reuven's money, a loan or deposit, and b'Ma'amad Sheloshtan Reuven told Shimon 'the money you have of mine, give it to Levi', Shimon must do so b'Al Korcho, even if he did not agree.

Beis Yosef (DH Kosav Rabeinu): The Riva and R. Tam say that it works b'Al Korcho. The Ran refutes his proofs. Sefer ha'Terumos agrees with those who argue with R. Tam. The Rosh says so in a Teshuvah (69), but in his Pesakim he agrees with R. Tam, and also the Rashba (2:378) does.

Shach (28): In Gitin (13b DH Omar), the Rashba argues with R. Tam. However, Teshuvas ha'Rosh (69:9) is like R. Tam, like he wrote in his Pesakim! (Note: Teshuvah 69:1 rejects R. Tam's proof.) 'Ma'amad Sheloshtan' connotes that Shimon consents, like the Nimukei Yosef (Bava Basra 70a DH Sholach) says. Also the Ro'oh, Ritva a Ba'al ha'Itur and Yam Shel Shlomo require Shimon's consent. If it were not needed, why would we require his presence? It would suffice to inform him! The Shulchan Aruch brought this opinion in Sa'if 5. I do not know why he did not bring it here.

Note: In Sa'if 5, the Shulchan Aruch says that Shimon cannot say that he will give to Levi only when he wants, and says that some disagree.

SMA (16): The dissenting opinion (here) holds that Shimon can say that he does not want to be the borrower of Levi, for Levi is harsher than Reuven.

Note: This does not explain why he can refuse regarding a deposit. Perhaps he fears lest it be lost due to negligence, and then he will owe its value.