Gemara

126b (Mishnah): If one said 'Ploni my Bechor will not receive a double portion', or 'Almoni my son will not inherit with his brothers', this does not take effect, for he stipulated against the Torah.

If one stipulated how much each son should receive, and gave to some sons more than others, or gave the Bechor as much as the others, this takes effect. If he said that this was their inheritance, it does not take effect. If he wrote at the beginning, middle or end that it is a gift, it takes effect.

130a (Mishnah): If Reuven said 'Ploni (a stranger) will inherit me', and he has a daughter, or he said 'my daughter will inherit me', and he has a son, this does not take effect;

R. Yochanan ben Brokah says, it takes effect if he gives to someone who could inherit him.

(Rava): R. Yochanan ben Brokah learns from "b'Yom Hanchilo Es Banav" - the Torah allows the father to bequeath to anyone he wants.

Question (Abaye): We learn that from "Lo Yuchal Levaker" (he cannot command that a Pashut (regular son) will inherit like the Bechor should, but he can bequeath as he wishes among his sons)!

Answer: We need that verse for the following law.

(Beraisa - Aba Chanan): A Pashut inherits Ra'uy (property that was destined to come to the father), but a Bechor does not. A father can bequeath to any son he wants.

Suggestion: Perhaps all the more so, he can give the extra portion of the Bechor to another son!

Rejection: "Lo Yuchal Levaker" teaches that he cannot.

(Rav Yehudah, Rava, R. Zerika citing Rav): The Halachah follows R. Yochanan ben Brokah.

R. Aba: (A case occurred, and) Rav ruled like R. Yochanan.

Rishonim

Rif (58b): Yochanan ben Brokah holds that the Torah allows one to bequeath to anyone he wants. This is when there is no Bechor. If there is a Bechor, and he gave to some sons more than to others, or gave to the Bechor as much as to the others, and called this inheritance, his words have no effect.

Nimukei Yosef (57b Sof DH Masnisin): If one gave to some sons more than others, or gave the Bechor as much as the others, and called this inheritance, it does not affect the Bechor, but it is fulfilled for the Peshutim. If he specified particular land for each son, they give proportionally, so the Bechor receives his double portion. If he did not specify land for each son, the Bechor gets a double portion in one place.

Rambam (Hilchos Nachalos 6:2): If one said 'Ploni my Bechor will not receive a double portion', this does not take effect.

Rambam (3): If he said 'Ploni my son will inherit half my property, and the rest of my sons will inherit the other half, his words are fulfilled. However, if he said that his Bechor 'will inherit like a Pashut' or 'he will not receive a double portion', or 'he will not inherit double with his brothers' this does not take effect, for it says "Lo Yuchal Levaker (he cannot make the son of the beloved wife to be the Bechor). He will acknowledge the son of the hated wife (to be the Bechor).'

Magid Mishneh: The Mishnah says 'if he gave to some sons more than others, or gave the Bechor as much as the others, this takes effect.' The Mishnah says that if he called this inheritance, it does not take effect, for he equated the Bechor to the others. If there is no Bechor, whatever he says takes effect, even if he called it inheritance. The Rambam says that one can decree that one son inherit all or half when there is no Bechor. If there is a Bechor, what he says does not affect the Bechor, for he called it an inheritance. Even though he did not mention the Bechor, since it decreases the Bechor's share, "Lo Yuchal Levaker" applies. The Ri mi'Gash says so, and adds that when there is a Bechor, just like the command is Batel regarding the Bechor, it is Batel regarding the Peshutim. Acharonim disagree, and say that the other brothers lose, in order that Ploni will get what was commanded for him, and the Bechor will get what he is entitled to. Here, the Rambam's opinion is not clear. From Halachah 5, it seems that he holds like his Rebbi (the Ri mi'Gash).

Rambam (5): If a Shechiv Mera divided his property and gave for a gift more to one son and less to another and equated the Bechor to them, his words are fulfilled. If he said that it is an inheritance, his words have no effect.

Rosh (8:28): Yochanan ben Brokah holds that the Torah allows the father to bequeath to anyone he wants regarding Peshutim. He agrees that he cannot change the Bechorah.

Poskim

Shulchan Aruch (CM 281:4): If one said that his Bechor 'will inherit like a Pashut', or 'he will not inherit double', this does not take effect, for it says "Lo Yuchal Levaker."

Gra (15): This is even like R. Yochanan ben Berokah (130a).

Ketzos ha'Choshen (4): A case occurred in which Yakov's Bechor Reuven died and left a son Chanoch, and before Yakov died, he commanded 'my son Shimon and Chanoch will divide my property equally.' The Maharit (CM 71) said that the command is Batel. Saying that they should divide is like an expression of inheritance, and one cannot change the extra share of Bechorah. However, the Ramban (Devarim 21:16) says that one cannot do so "Al Pnei... ha'Bechor", i.e. while the Bechor is alive. If he died, the father can command like when there is no Bechor. The Maharit did not cite the Ramban. Presumably, had he seen it, he would agree.

Nesivos ha'Mishpat (Bi'urim 5): If he commands about inheritance, also regarding a Pashut his words have no effect! Perhaps regarding a Bechor, even if he gives a gift and says that the sons will inherit the rest, his words have no effect, but regarding Peshutim it would take effect.

Rema: Even where the custom is that the Bechor does not receive double, we do not follow the custom, for it is against Torah law.

Gra (16): Even though the Mishnah (2a) says 'we follow the local custom', Tosfos (2a DH bi'Gvil) says that this includes a wall of laurel and palm branches, but anything less than this is an inferior custom and we do not follow it. Maseches Sofrim (14:18) says that a custom of Chachamim overrides Halachah, but a custom without a proof from Torah is like an error in judgment. All the more so, a custom that uproots Torah law is Batel!

Shulchan Aruch (6): If a Shechiv Mera has a Bechor and Peshutim, and he commanded that a Pashut inherit extra, e.g. Ploni my son will inherit this amount, his words have no effect. Some say that the Peshutim divide like he said, and each gives the proper amount from his share to pay to the Bechor.

Ran (129a DH Hishveh, cited in Beis Yosef DH v'Chosav): The Mishnah says 'if he gave for a gift more to one son and less to another, and equated the Bechor to them, his words are fulfilled. If he said that it is an inheritance, his words have no effect.' The Rashbam (DH 126b v'Im) explains that it does not work to equate the Bechor, nor to give more to a Pashut. This is like Chachamim, unlike R. Yochanan ben Berokah. Some say that all agree to the Mishnah. His words have no effect regarding the Bechor. R. Yochanan ben Berokah admits regarding the Bechor. The Re'em says that even according to R. Yochanan ben Berokah, the entire command is Batel. Since it is Batel regarding the Bechor, it is Batel regarding the Peshutim. It seems that the Rambam agrees. This is wrong. It is Batel regarding the Bechor, but his words are fulfilled regarding the Peshutim. R. Yonah (129a DH v'Im) says so. The Peshutim give proportionally and pay the Bechor. The Acharonim agreed

Tur: Some say that the division among the Peshutim is fulfilled, and they give proportionally and pay the Bechor. He is like a creditor, who collects proportionally from them. The Rosh holds like this.