Gemara

64b (Rav Yehudah): If a child knows to discard a rock but keep a nut, he can acquire for himself, but not for others. If one can deposit an item by him and he will return it later, he can acquire for himself and for others.

Shmuel: Both of these children have the same law.

Rav Chisda: He means that either can acquire for himself, but not for others.

Question (Rav Chinena Vardan - Mishnah): The following may acquire Shituf Mavo'os (a kind of Eruv): ... or a female Yisrael slave.

A female Yisrael slave must be a minor, yet she can acquire for others!

Answer: Shituf Mavo'os is mid'Rabanan. Chachamim were lenient to allow her to acquire, but mid'Oraisa, she cannot acquire.

Rav Chisda: Rav Chinena could have countered that decrees of Chachamim are patterned on mid'Oraisa laws.

Bava Metzia 10a (Reish Lakish): A girl (minor) does not acquire through her Chatzer, nor through her four Amos.

(R. Yochanan): She acquires through her Chatzer and her four Amos.

10b - Opinion #1: Regarding a Get, all agree that her Chatzer acquires like her hand. They argue about a Metziah. R. Yochanan learns from Get to a Metziah, Reish Lakish does not.

Opinion #2: All agree that regarding a girl we learn from Get to a Metziah. They argue about a boy. R. Yochanan learns a boy from a girl; Reish Lakish does not.

Opinion #3: R. Yochanan and Reish Lakish do not argue. They discuss different things. (Reish Lakish discusses a boy, and R. Yochanan discusses a girl. Alternatively, Reish Lakish discusses a girl acquiring a Metziah, and R. Yochanan discusses acquiring a Get.)

12a: R. Yosi agrees that a minor cannot acquire mid'Oraisa!

(Mishnah): For the sake of Shalom, if a Cheresh, lunatic or minor picked up a (Hefker) Metziah, it is considered theft to take it from him;

R. Yosi says, it is absolute theft.

(Rav Chisda): It is absolute theft mid'Rabanan.

R. Yosi says that Beis Din makes one return it to them. Chachamim say, Beis Din does not make one return it.

Kidushin 19a (Beraisa - R. Yosi b'Rebbi Yehudah): "Ya'adah v'Hefdah" - one can do Yi'ud only if the Amah could be redeemed.

This is when enough time remains (in her six years of service) for her to do a Perutah's worth of labor.

(Rava): He holds that the initial money was not given for Kidushin (he is Mekadesh her now by pardoning her remaining servitude). We infer that a man can authorize his (minor) daughter to receive her own Kidushin money.

Bava Basra 156b (Mishnah - R. Eliezer): We may acquire on behalf of a minor, but not on behalf of an adult. (An adult could acquire for himself);

R. Yehoshua says, we may acquire for a minor, all the more so for an adult!

Sukah 46b (R. Zeira): One should not be Makneh (transfer ownership of) his Lulav to a child on the first day, because a child acquires, but he cannot be Makneh.

Rishonim

Rif and Rosh (Bava Metzia 5a and 1:29): The Halachah is, a girl acquires through her Chatzer and her four Amos. The Torah includes her Chatzer like her hand. We learn from Get to Metziah. We do not learn boys from girls.

Rosh: This is like the last opinion in Bava Metzia (Reish Lakish and R. Yochanan do not argue), or like R. Yochanan according to Opinion #1.

Ran (DH Gemara): Even though four Amos do not acquire a Get, since we learn from Get that a girl has a Chatzer, Chachamim enacted four Amos for her. This refers to after Nisu'in, or an orphan. A girl in her father's Reshus cannot receive her Get; her father does. In buying and selling, a boy acquires mid'Rabanan, through Da'as Acheres Makneh (when an adult gives to him), what comes to his hand. We did not enact Chatzer or four Amos for him.

Rebuttal (Shach CM 243:6): A minor acquires even a Metziah mid'Oraisa. We learn from Bava Metzia 10b. We conclude that they argue about whether or not a minor acquires through a Chatzer, but all agree that he himself can acquire a Metziah. Tosfos (11a DH Yalfinan) says that we 'learn' from Get, i.e. mid'Rabanan. This is difficult. The Gemara connotes that we learn from a verse! Also, since we learn Yad, we should also learn Chatzer! The Rif and Rosh connote that we learn mid'Oraisa. A boy has a Yad mid'Oraisa; the only question is whether or not we learn Chatzer from a girl. The Gemara (12a) proved from the Mishnah of Darchei Shalom that R. Yosi agrees that a minor cannot acquire mid'Oraisa. This refers to a child below the age when he discards a rock but keeps a nut. The Yerushalmi says so. We did not say that Mishnah discusses a child above this age, for then Chachamim would agree that taking his Metziah is absolute theft!

Defense (Magen Sha'ul, Leshonos ha'Rambam 36:3, cited in R. Akiva Eiger on the Shach): The Yerushalmi teaches a third level of maturity, when a child knows to store away a nut. Chachamim agree to R. Yosi that taking such a child's Metziah is proper theft mid'Rabanan. There is no source that a minor can acquire mid'Oraisa without Da'as Acheres Makneh.

Rif and Rosh (Gitin 27b and 5:19): Chachamim enacted that Pa'utos can buy and sell for their needs.

Rambam (Hilchos Mechirah 29:1): Mid'Oraisa, a child cannot buy or sell. Chachamim enacted that he can buy and sell Metaltelim Kedai Chayav.

Magid Mishneh: One may not take the Metziah of a minor due to Darchei Shalom. Mid'Oraisa, he cannot acquire. Some say that a minor acquires mid'Oraisa through Da'as Acheres Makneh. The Gemara connotes like the Rambam. We learned that an adult can be Zocheh, but a minor cannot. One can be Zocheh for an adult, but not for a minor. It seems that the Rambam holds that he acquires a gift mid'Oraisa, but his purchase is invalid, for he cannot Makneh the money to the seller. The Rambam in Hilchos Zechiyah (4:7) and Hilchos Lulav (8:10) supports this.

Rambam (Hilchos Lulav 8:10): We do not give a Lulav to a child on the first day of Sukos.

Question (Kesef Mishneh): The Ran says that this is only if the child is below Pa'utos, i.e. six or seven. Why didn't the Poskim mention this?

Answer (Magid Mishnah, Mechirah 29:1): The Rambam holds that Pa'utos acquire a gift mid'Oraisa, but they cannot be Makneh mid'Oraisa.

R. Mano'ach: Pa'utos can acquire mid'Rabanan and return mid'Rabanan. If an adult acquires for any minor, this is mid'Oraisa, and there is no way to return it mid'Oraisa.

Question: How can a minor receive her own Kidushin? A minor cannot acquire mid'Oraisa, like we say in Bava Metzia 12b!

Answer (Rosh Kidushin 1:25): When an adult is Makneh, a minor can acquire mid'Oraisa, like we find in Gitin 64b. Rav Chisda said that a minor can be Zocheh only for himself. We asked from a Beraisa to show that he can be Zocheh even for others. We answered that it is only mid'Rabanan. This implies that Rav Chisda holds that he can be Zocheh for himself mid'Oraisa, and Rav Yehudah holds that he can be Zocheh even for others mid'Oraisa. We also learn from Sukah 46b, which says that one should not be Makneh his Lulav to a minor, because a child acquires, but he cannot be Makneh. I.e., through Da'as Acheres Makneh he acquires mid'Oraisa.

Note: It is not clear how the Shach (above) said that he holds like the Rosh.

Poskim

Shulchan Aruch (OC 658:6): One should not give his Lulav to a child on the first day before the giver was Yotzei, because a child acquires, but he cannot be Makneh (back) mid'Oraisa. Some permit if he reached the age of Pa'utos.

Bi'ur Halachah (DH Lo): The latter opinion holds that children acquire only mid'Rabanan even with Da'as Acheres Makneh, Pa'utos can be Makneh back mid'Rabanan. The first opinion holds that Pa'utos acquire mid'Oraisa with Da'as Acheres Makneh, but they cannot be Makneh mid'Oraisa,

Shulchan Aruch (EH 37:7): A man can authorize his (minor) daughter to receive her own Kidushin.

Rema: If a man is Mekadesh her with a document, he writes 'your daughter is Mekudeshes to me' (not 'you are Mekudeshes to me').

Gra (21): The Ran says that her father can authorize her to receive Kidushin money. It is as if he told the Mekadesh 'put the money on the rock.' This does not work for a document of Kidushin. The Rema rules like the Rosh, who says that a minor can acquire mid'Oraisa, through Da'as Acheres Makneh. This helps even for a document.