Gemara

124a (Beraisa): A Bechor does not get a double share in Shevach (improvements to the property) after the father's death;

Rebbi says, he gets a double share in Shevach.

If they inherited a loan document, the Bechor collects an extra share.

Chachamim learn from "Lases Lo Pi Shnayim" - the Torah calls the extra share a gift. Just like a gift takes effect only after it comes to the receiver, also the extra share of the Bechor.

(Rami bar Chama - Beraisa): "B'Chol Asher Yimatzei Lo" excludes if the property went up in value by itself. The Bechor gets no extra share;

125b (Rav Papa): The Halachah is, a Bechor does not get an extra share in a loan owed to the father, whether it was paid with money or land.

(Rav Asi): If a Bechor took a portion like a regular son, he pardoned his extra share.

Question: What did he pardon?

Answer #1 (Rav Papa citing Rava): He pardoned his extra share in that field.

He holds that the Bechor does not own his extra share until they divide. (He cannot pardon what he does not yet own.)

Answer #2 (Rav Papi citing Rava): He pardoned his extra share in all the property.

He holds that a Bechor owns the extra even before they divide. (Since he pardoned his extra share in this field, he pardoned his extra share in all the property.)

Rav Papa and Rav Papi did not explicitly hear Rava say this. Rather, they derived their opinions from a case in which a Bechor sold his property and that of his brothers. His brothers went to eat dates of the property. The buyer hit them. Their relatives complained to Rava. Rava ruled that the sale is void.

Rav Papi understood that the sale of the brothers' property is void, but the sale of his own property stands. Rav Papa understood that the entire sale is void.

(Chachamim of Eretz Yisrael): If a Bechor sold (his extra share) before the property was divided, the sale is void.

They hold that the Bechor does not own his extra share until they divide.

The Halachah is, a Bechor owns his extra share even before they divide.

Mar Zutra of Darishba (a Bechor) divided a basket of peppers equally with his brothers.

(Rav Ashi): Since you pardoned your extra share in the peppers, you pardoned your extra share in all the property.

Bechoros 52a (Mishnah): A Yavam does not receive Shevach.

He is called "Bechor" (therefore, he inherits like a Bechor).

(Abaye): He does not receive Shevach between the death and Yibum, but he receives Shevach between Yibum and division. "Yakum Al Shem Achiv" - once he did Yibum, his brother's property is his.

(Rava): He does not receive even Shevach between Yibum and division, like a Bechor, who receives no Shevach before division.

Rishonim

Rif and Rosh (8:14): The Halachah is, a Bechor owns his extra share even before they divide. A case occurred in which a Bechor divided a basket of peppers equally with his brothers. Rav Ashi ruled that he pardoned his extra share in all the property.

Nimukei Yosef (DH Garsinan): Rava ruled that the Bechor's sale of his brothers' property was invalid, but the sale of his extra share was valid, and all the more so the sale of his regular share was valid. Alll Meforshim explain like this, except for the Rashbam (who says that only the sale of his extra share was valid). In Bechoros, we rule that a Bechor does not get Shevach before division. Here we discuss ownership of the property itself.

Me'iri (126b DH mi'Mah): The Rashbam saw that one opinion says that the sale did not work at all. We rule unlike this, for he owns the extra share even before division, but all agree that the sale of his regular share was void. This is wrong. That opinion only meant that the sale did not work for the extra share and the brothers' shares, but there is no reason it should not work for his regular share.

Rif: Someone rules like Rebbi that a Bechor gets a double portion in a loan. He brings a proof from here, that we rule that he owns his extra share even before they divide. This shows that it is as if it already came to his hands. One may not rely on this. We rule that it is as if it already came to his hands only regarding what was in the father's Reshus. This does not apply to a loan. Also Rav Hai Gaon says so.

Question (Rosh): Above (125b), we rule like Rav Papa, who says that a Bechor does not get an extra share in a loan owed to the father. This is like Chachamim, who say that a Bechor does not get a double share in Shevach, because the extra share is called a gift, and he owns it only after it comes to him!

Answer (Rosh): Really, Chachamim exclude Shevach from "b'Chol Asher Yimatzei Lo", like the Beraisa. On 124a, we said that they learn from "Lases Lo Pi Shnayim", because both verses are needed. Really, Chachamim hold that the property is in his Reshus even before they divide. He can pardon the extra share through mere words, for it is a gift.

Rambam (Hilchos Nachalos 3:6): If a Bechor sold his extra share before dividing, the sale stands, for he owns his extra share even before division. Therefore, if he divided part of the property with his brothers, either land or Metaltelim, and received a share like a regular brother, he pardoned his extra share in all the property and receives like a regular brother.

Me'iri (126a DH Zeh): If he didn't acquire his extra share before division, his pardon would not apply to what he does not own yet. Since we conclude that he owns his his extra share before division, if he sold it, the buyer acquired. If he sold it to his brothers, this is pardon, and no Kinyan is needed.

Poskim

Shulchan Aruch (CM 278:8): If a Bechor sold his extra share before dividing, the sale stands, for he owns his extra share even before division. Therefore, if he divided part of the property with his brothers, either land or Metaltelim, and received a share like a regular brother, he was Mevater (i.e. he was silent and pardoned something he could have claimed) his extra share in all the property and receives like a regular brother.

Beis Yosef (DH u'Piresh): The Rashbam explains that since it is a gift, he may decline it and not need pay an extra share of a debt against his father.

SMA (25): If he didn't yet acquire, his pardon would not show that he pardons his extra share in other property. This is why the Shulchan Aruch says 'therefore'.