Gemara

(Rava): If Shimon told Levi 'give a Maneh to Yehudah to acquire my property', this makes a proper sale, like we find regarding an Arev (guarantor. He is obligated to pay a loan even though he did not receive the money. Likewise, a seller can transfer ownership of his land through a transfer of money, even if he does not receive the money).

Kidushin 6b (Rava): If Leah told Reuven 'give a Manah to Ploni, and I will be Mekudeshes to you', we learn from the law of an Arev that this works.

An Arev obligates himself (to pay a loan, if the lender does not), even though the Arev does not benefit. Likewise, Leah can acquire herself to Reuven without receiving the money.

8b (Beraisa): If one said 'be Mekudeshes to me with a Maneh', and she said 'give it to my father', 'to your father' or 'to Ploni', she is not Mekudeshes. If she said 'on condition that he receive it for me', she is Mekudeshes.

Rishonim

Rambam (Hilchos Ishus 5:21): If Leah told Reuven 'give a Manah to Ploni for a gift, and I will be Mekudeshes to you', and he gave, and said 'you are Mekudeshes to me with the Hana'ah of this gift that I gave due to your words', she is Mekudeshes. Even though she did not receive anything, she benefits from her desire being fulfilled and Ploni benefited due to her.

Magid Mishneh: Also the Rashba said so. We must say so, for if he did not say so, giving to someone else due to her words is no better than when he gave to her and she said (the Amirah, that she will be Mekudeshes through this), which is only Safek Kidushin.

Ran (Kidushin 3a DH Ten): The Rambam says that he said 'you are Mekudeshes to me with the Hana'ah of this gift that I gave due to your words.' If not, this is like when he gave the money and she said the Amirah, which is only Safek Kidushin. However, some say that even if he did not say anything, it helps, since she said 'and I will be Mekudeshes to you' and he gave due to her words. This is no worse than wen they were discussing her Kidushin. This works even if he did not specify (when he gave to her). This is unlike when he gave to her and she said, for there he gave first, and it is known he gave for Kidushin only due to her words, so her words finished the Kidushin. Therefore, it does not work. Here, he does the entire act of Kidushin. Through his giving, the Kidushin is finished without any other words. Her words are like speaking with him about Kidushin, which works even (if the money was given) Stam. The Rambam's opinion is primary. Surey, when he gave and she said, it is a Safek because she takes herself to him, i.e. when she says at the time of the giving. After he gave, his silence is no better than her silence. If he gave a deposit, and later said 'you are Mekudeshes to me' and she was silent, Rava (12b) says that her silence after the money was given is nothing. All the more so here, if he initially gave Stam, letter of the law she acquires the money like a gift. Surely her words and his silence does nothing. Rather, the Safek is when he gave and she said at the time he gave, even though this is why he gave. This is unlike discussing her Kidushin. That is when he said. If he did not say anything, even though his giving proves that he agrees to her words, it does not work. His silence is like her silence (after the money was given) when he gave and later said and she was silent. Normally, silence is considered consent. However, whenever he did not say anything, perhaps this is not 'when a man will take a woman.' Perhaps you wil say that her silence shows consent. Since she becomes forbidden, if she objected, she should protest. Regarding a man (when he gave and she said), since he can marry another woman if he wants, he is not concerned if it looks like he consents, so he could be silent even if he objects. (Here, when she said 'give a Manah to Ploni and I will be Mekudeshes to you', even if he was silent he agreed to her words, for he gave only after she told him. Therefore, even if he did not say anything at the time of giving, she is Mekudeshes.) If so, the Safek is not due to the requirement that he take her, rather, due to a Safek whether he consented. The Sugya is unlike this.

Rosh (Kidushin 1:13): If she said 'put a Manah on the rock (or give a loaf to the dog), and I will be Mekudeshes to you', perhaps she is Mekudeshes due to the law of Arev. Or perhaps, it must be like an Arev, in which another person received. The latter seems correct, but it is proper to be stringent.

Ran (Kidushin 4b DH Haysah): The Ramban says that when she said 'put a Manah on the rock', even if she said 'and I will be Mekudeshes to you', this is nothing. He did nothing due to her words. However, if she said 'give a loaf to the dog, and I will be Mekudeshes to you', she is Mekudeshes due to the law of an Arev, for he spent money due to her. Some say that Arev is only when he gives to someone with Da'as (intellect). He becomes liable through the other's acceptance. It does not apply to one who throws away money. Some Tosafists and the Rashba hold like this.

Tosfos (Kidushin 8b DH Tenam l'Aba): Why is this different than 'give a Manah to Ploni, and I will be Mekudeshes to you'? There, she spoke first. We can say that she intended to become Mekudeshes. Here, he spoke first, and she said 'give them to whom you want.' We can say that she does not intend for Kidushin. She jests with him, and she is not concerned.

Poskim

Shulchan Aruch (EH 29:2): If Leah told Reuven 'give a Manah to Ploni, and I will be Mekudeshes to you', and he gave to Ploni and said 'you are Mekudeshes to me with the Hana'ah of this gift that I gave due to your words', she is Mekudeshes.

Beis Yosef (DH Amrah): Rashi and the Rambam explain that when he gave to Ploni, he said 'be Mekudeshes to me.' The Ran says that this is primary. R. Yerucham agrees, and says that alternatively, they were discussing Kidushin.

Bach (DH v'Nireh): It helps only when he said 'be Mekudeshes to me' within Toch Kedei Dibur (the time to say three or four words) of when he gave. It it was after Kedei Dibur, this is like silence after the money was given, and she is not Mekudeshes.

Rebuttal (Chelkas Mechokek 4): We say that silence after the money was given is nothing only when he initially gave a deposit, and later said that the deposit should be Kidushin. Then, surely her silence is nothing. Here, she told him to give to Ploni, and he fulfilled her Shlichus. If afterwards he says 'you are Mekudeshes to me with what I gave due to you', informing her is like giving money. At that time she gets Hana'ah that her words were fulfilled. Even if she already knew that he fulfilled it, she is Mekudeshes. This is no worse than discussing her Kidushin.

Beis Shmuel (6): The Taz agrees. Why does the Chelkas Mechokek say that this is no worse than discussing her Kidushin?!

Taz (5): We learn from the Magid Mishneh that if she said, and he said 'yes', this helps, even if he gave later. This is like discussing Kidushin. We attribute the giving to what they said before. However, if only she said that he should give to Ploni for Kidushin, this is not discussing Kidushin.

Rema: If they were discussing Kidushin, even if he gave Stam due to her command, she is Mekudeshes. This is only if she initially said 'give a Manah to Ploni.' If he first said, and she said 'give to Ploni', see 30:8

Gra (3): The Rashba, Ramban and Ran say that she must say 'I will be Mekudeshes it you' to answer Tosfos' question. (On 8b, she never mentioned Kidushin.) The Mechaber rules like them. The Rema says that she must speak first. This is like Tosfos.

Rema (30:11): If she said 'give a loaf to the dog, or put a Manah on the rock, and I will be Mekudeshes to you', some say that it is as if she said 'give a Dinar to Ploni', like explained above (29:2). It is proper to be stringent.

Chelkas Mechokek (18): One should be stringent to consider it Safek Kidushin, unlike the opinion that regarding a dog, it is Vadai Kidushin.

Beis Shmuel (18): Letter of the law, she is not Mekudeshes for the law of Arev does not apply.

Avnei Milu'im (12): The opinion that 'put a Manah on the rock' works holds that Din Arev applies even if she said 'throw it to the sea', since he spent money due to her. The Tur equates on the rock to giving to a dog. He discusses a rick that is not guarded, so it is like throwing money to the sea. The Ramban (cited in the Ran) discusses a guarded rock, so he did nothing.