Gemara

(Beraisa - R. Yosi): If a Kohen died and left sons and his wife was pregnant, her Tzon Barzel slaves do not eat Terumah, because the fetus owns a share. A fetus forbids to eat Terumah, but does not permit;

R. Shimon says, both types of slaves eat.

Question: Why does R. Shimon permit? The fetus owns a share!

Answer #1: R. Shimon is not concerned for the minority (that the fetus is a viable male. Half of all fetuses are male, and some of these are Nefalim.)

Answer #2: Really, he is concerned for a minority, but we fix things like Rav Nachman:

(Rav Nachman citing Shmuel): When orphans come to divide their father's estate, Beis Din appoints an Apotropos (overseer), and they pick for them a nice share. When they grow up, they can protest (demand a new division);

Rav Nachman himself holds, they cannot protest. If they could protest, (the enactment of) Beis Din would be weak!

(Here, we give other property to the fetus (on condition that he is a male), so he has no share in the slaves.)

Suggestion: R. Yosi and R. Shimon argue about whether we make an enactment like Rav Nachman.

Rejection: No, all agree to it. They argue about whether or not we are concerned for a minority (when the enactment was not done).

Answer: (They did not err about the value.) They erred about location (e.g. an orphan received a portion far from property that he inherited from his mother's father).

Kidushin 42a (Rav Gidal): "One Nasi (for each tribe will acquire a portion of Eretz Yisrael for his tribe)" teaches that a Shali'ach can act on behalf of others.

Objection: The Nesi'im could not have been Sheluchim. They also acquired on behalf of minors, who cannot make Sheluchim!

Correction (Rav Gidal): "One Nasi" teaches that Reuven can acquire to benefit Shimon in Shimon's absence.

Objection: The acquisition of shares of Eretz Yisrael was not beneficial for everyone. Some people prefer land in the valley, and others prefer in the mountain!

Correction (Rav Gidal): "One Nasi" teaches that if orphans come to divide their inheritance, Beis Din appoints an Apotropos for them;

The Apotropos is empowered to do things which may have a detrimental result, if the intent is to benefit the orphans.

Rishonim

The Rif (Kidushin 17a) brings Rav Nachman's enactment.

Ran (Gitin 16b DH Halachah): One Apotropos is appointed for each child and he picks a nice share for his child, in order that the shares will be equal.

Rambam (Hilchos Nachalos 10:4): If a man left adult and minor orphans and they want to divide their father's estate in order that the adults will receive their shares, Beis Din appoints an Apotropos for the minors and he picks for them the nice share. . When they grow up, they cannot protest, for the division was according to Beis Din.

Magid Mishneh: These words 'the division was according to Beis Din' show that the Rambam holds like R. Tam, who says that the Apotropos divides only according to Beis Din's estimation.

Rosh (Kesuvos 11:18): Some say that Rav Nachman's law is even if only one orphan wants to divide, for the Gemara (Kidushin 42a) cited it regarding the division of Eretz Yisrael in which there were babies who owned shares. This is not a solid proof, for that division was through Hash-m's command and the Urim v'Tumim. Some prove from Yevamos, in which we apply Rav Nachman's law even when one of the heirs is a fetus! This is not a proof, for there the division benefits the fetus. It enables the slaves to eat Terumah, which is cheap, and increases the value of the estate. Also, it is no proof that we make an Apotropos to divide if one of the sides protests. R. Tam says that we do not divide when one of the heirs protests. It seems that the entire discussion is when all of the orphans are minors and we need an Apotropos to oversee the property, therefore we do not divide it without all of their consent. However, if some are adults and they want to receive their share to work and guard it, surely we hearken. Why should they lose due to the minors?! Shmuel does not discuss when all of them are minors, for he would not say 'they came to divide'. A minor's actions have no effect! Rather, Beis Din decides whether it is good or bad for them to divide. Rather, Shmuel discusses when adults want to divide. He teaches that Beis Din accedes.

Ran (Kidushin 17a DH Yesomim): Surely Shmuel's enactment is not when all of the heirs are minors. If so, what good is the division? Anyone can protest when he matures! Also regarding produce until they mature it is no better than if one Apotropos was handling the entire property for all of them. The primary text says 'Borerin', i.e. Beis Din and the Apotropos together divide the property. Even according to the texts that say 'Borer' (according to Hagahos ha'Bach), it means that the Apotropos seeks a good share for the orphans. All agree that it is done with Beis Din. Whenever there is a Safek the adults must pardon, for minors cannot pardon.

Ritva (Kidushin 42a DH Omar): Dividing now can be bad for the minors. After they mature they could be more exacting about the division, and perhaps they would prefer a different portion. Also, the Mazal is better when all the property is together. Nevertheless, we are concerned for the loss of the adults, so we divide now. The Apotropos takes one combined portion for all the minors. If each received his portion now, we would appoint one Apotropos for each.

Rosh (ibid.): They appoint an Apotropos to pick a good share through a lottery and the estimation of Beis Din. R. Tam explains that picking a good share applies even when they divide through a lottery. E.g. we ensure that each one gets his share in one place, and arrange rights to have windows, ladders and rights to pass through the others' shares. We do not divide something to which the law of Gud O Agud applies (buy my share or let me buy your share). If they did, the Gemara should have said that they erred regarding Gud O Agud, rather than about the directions!

Tosfos (Kidushin 42a DH u'Vorerin): The Ri said that the Apotropos is in place of the orphans to divide without Beis Din and without a lottery and even matters of Gud O Agud. R. Tam disagrees, for it is no exertion to make a lottery! They need Beis Din's estimation, but may not divide Gud O Agud. The Ri retracted and agreed with R. Tam.

Ritva (DH umid'Kamrinan): R. Tam says that they can divide through Gud O Agud. (This is unlike how Tosfos cites R. Tam.) If not, since they use a lottery, what depends on the Apotropos' choice? Also, the division of slaves in Yevamos is Gud O Agud. The Ri disagrees, for Gud O Agud is like a sale, and Apotropsim cannot sell. The case of the slaves is an exception, to save the fetus a loss if the slaves must eat Chulin. Also, it is not clear that the fetus has a share in the slaves at all (perhaps the fetus is a female).

Poskim

Shulchan Aruch (CM 110:1): We do not collect debts from heirs less than 13 years old. If some of the heirs are adults and some are minors, Beis Din appoints an Apotropos to divide the property, and the creditor collects from the adults.

Gra (3): Rav Nachman's enactment is when some of the orphans are adults.

Shulchan Aruch (289:1): If a man left adult and minor orphans and they want to divide their father's estate in order that the adults will receive their shares, Beis Din appoints an Apotropos for the minors and he picks for them the nice share.

Beis Yosef (DH Kosav ha'Rashba): If the widow is pregnant, she can stop the orphans from dividing the property, for perhaps she is pregnant with a male. They can divide only if an Apotropos is appointed on behalf of the fetus, like the case in Yevamos.

SMA (1): If they do not divide, the adults care for the estate and all profits are shared.

Rema: Some say that they must divide through a lottery.

Rema: An Apotropos cannot divide without Beis Din, even if their father appointed him, unless he was appointed explicitly for this. Beis Din cannot divide something to which Gud O Agud applies. Some disagree and permit.

SMA (5): Gud O Agud is like a sale. The Apotropos cannot sell their property.

Rema: If all the brothers are minors they do not divide until they mature, unless Beis Din effect sees that it is beneficial for them to divide now. When the orphans are above 13 they can divide by themselves. This is not like a sale.

Source: Beis Yosef (DH Kasuv) citing Meisharim (26:2).

SMA (7): If it would be like a sale, the orphans could not divide before 20 years of age, The Rosh permits a very sharp orphan to sell before 20.