1)ONE WHO GAVE AN UNSPECIFIED SHARE
(a)Gemara
1.Obviously, if Reuven said 'Ploni will divide my property', he gets half.
2.Question: If he said 'give to him a portion of my property', what is the law?
3.Answer (Ravina bar Kisi - Beraisa - Sumchus): If Shimon said 'give to Ploni a portion in the pit', he gets a quarter. If he said 'for the barrel', he gets an eighth. If he said 'for the pot', he gets one part in 12. If he said 'for the pitcher', he gets one part in 16.
(b)Rishonim
1.Rif: We learn from the Beraisa that if one said 'give to Ploni a portion of my property', he gets a quarter, like when one said Stam (without specifying) 'give to Ploni a portion in the pit.' People do not say 'a portion' for less than a quarter. It refers to a pit of water. We do not know the reasons why one who was given a portion for the barrel, pot or pitcher gets an eighth, 12th or 16th, therefore, we do not learn from them to other laws. Some explain differently; what I wrote is correct without any doubt.
i.Ramban (63a DH ha'Omer): Perhaps the Gemara knew that it is normal for eight people to divide a pit for barrels, and 12 to divide for pots, and 16 to divide for pitcers, and this suffices. We do not distinguish based on the size of the pit.
ii.Note: They must say that the Gemara brought the Seifa to teach these laws, even though they are not relevant to the question.
2.Rambam (Hilchos Zechiyah 11:7): If a Shechiv Mera said 'Ploni will divide in my property', he gets half. If he said 'give a portion to Ploni in my property', he gets one part in 16. Some say that he gets a quarter.
i.Ra'avad: The Rif says that he gets a quarter. This is primary.
ii.Magid Mishneh: Some say that when he said Stam 'give a portion', he gets the smallest portion (that the Beraisa mentions), one in 16. The Ga'on says that he gets a quarter. The Rif says that this is primary.
3.Rosh (4:6): A Tosefta (7:5) teaches that if he said 'give a portion to Ploni in my property', he inherits with (i.e. like one of) the sons. It refers to a Shechiv Mera. Our Gemara discusses a healthy giver. The Rashbam (63a DH Sumchus) says that we are unsure if 'portion' refers to half, or an arbitrarily small share. Sumchus holds that when we are in doubt, we divide the money. The Halachah follows Sumchus, for Stam Mishnayos (Bava Kama 46a, Bava Metzia 100a) are like him. The Ri rules like Chachamim, who say that ha'Motzi mi'Chavero Alav ha'Re'ayah, for Rav Nachman holds like them (Bava Metzia 102a), and the Halachah follows Rav Nachman in monetary laws. Even though R. Shimon ben Gamliel holds like Sumchus in the Mishnah (100a), and there are only three cases in which the Halachah does not follow R. Shimon ben Gamliel in Mishnah (and this is not one of them), this rule does not override a ruling of Amora'im. Also the Rif rules like Chachamim. He explains that the Gemara resolves its question from Sumchus because it is not due to Safek. Rather, people do not say 'a portion' for less than a quarter. However, the Rif could not explain why one who was given a portion for the barrel, pot or pitcher gets an eighth, 12th or 16th. Therefore, the Rashbam's Perush is primary. All the Shi'urim are due to Safek. In any case, this does not prove that the Halachah follows Sumchus. The Gemara brought Sumchus' Beraisa to teach that there is a Safek about what he meant. We know that the Halachah follows Chachamim, and ha'Motzi mi'Chavero Alav ha'Re'ayah (perhaps he meant a very small amount).
4.Rashbam (63a DH Tenu): A Tosefta (7:5) teaches that if he said 'give a portion to Ploni in my property', he inherits with (i.e. like one of) the sons. Our Gemara discusses when the giver has no sons. Even if he has other heirs, one is not concerned for other heirs as much as for his sons. Alternatively, Ravina discusses one who said 'give to Ploni my son a portion in my property, and Almoni will get the rest.' Alternatively, the Gemara did not know the Tosefta. Had it known it, it would have brought it. One can say that the Tosefta is like Chachamim, who argue with Sumchus. Alternatively, the Gemara knew the Tosefta, but we hold like Sumchus.
5.Tosfos (63a DH Ein): Surely, even if he means 'any amount', he gives a gift of some worth, e.g. a Revi'is. The Gemara did not bother to mention it.
(c)Poskim
1.Shulchan Aruch (CM 253:24): If a Shechiv Mera said 'give a portion to Ploni in my property', he gets one part in 16. Some say that he gets a quarter.
i.Beis Yosef (DH v'Zeh Lashon ha'Ran, citing the Ran): The Rambam says that he gets one part in 16. Since for other matters we are unsure, Ploni receives the smallest amount, like one who received for a pitcher.
ii.SMA (52): The Rambam explains that Ravina settled the question from the Seifa. Even though we do not learn from these matters to other things, we never find that 'a portion' ever refers to less than a 16th, so he receives a 16th. The other opinion in the Rambam learns from the Reisha that he receives a quarter.
2.Rema: If a Shechiv Mera was dividing his estate among his sons, and said 'Ploni will receive a portion in my property', he gets like one of the sons.
i.Gra (49): This is like both answers of the Rashbam (to resolve the Tosefta with the Gemara). L'Halachah, both answers are one.
ii.Drishah (40): Surely the Tosefta discusses a Shechiv Mera, for it mentions inheritance. A healthy person would not say that Ploni should inherit him. We must say that he specified that the rest go to his sons (or Almoni), for if a Shechiv Mera gave only some of his property, it is like a gift of a healthy person.
3.Shulchan Aruch (25): If a Shechiv Mera said 'give to Ploni a portion in my pit of wine', he gets a quarter. If he said 'give to him a portion for the barrel', gets an eighth. If he said 'give to him a portion for the pot, he gets a 12th. If he said 'give to him a portion for the pitcher, he gets a 16th, for he showed that he intended for a small gift. We do not learn from these Shi'urim to other matters.
i.Gra (50): The Rif holds that the laws are not due dividing the money when in Safek, for Sumchus says so only when the property is in a Simta (neither's Reshus) or the Muchzak is unsure.
4.Rema: Some say that in all these cases, he has an arbitrarily small share. This applies only to a gift.
i.SMA (52): This is the Rosh's opinion, who holds that he receives an arbitrarily small share. Ravina learned from the Beraisa either because he holds like Sumchus, or he holds like Chachamim and learns about their opinion from Sumchus. The Rema said 'he has an arbitrarily small share.' To be precise, he should have said 'he gets an arbitrarily small share', i.e. because we are unsure how much he has! Ir Shushan says that the Rema does not refer to Sa'if 24. This is wrong. This opinion holds that he always gets an arbitrarily small share.
5.Rema: For such cases of sales, the price reveals how much he sold.
i.Beis Yosef (DH v'Zeh Lashon Rav, citing the Rashba): R. Chananel says so. Also the Gaon in Sefer ha'Mekach says that in a sale, he acquires a portion exactly according to the price.
ii.Beis Yosef (DH v'Zeh Lashon ha'Ran, citing the Ran): The Tosefta says that 'a portion' refers to a quarter regarding a sale! These Ge'onim must hold that the Gemara changed the text of the Tosefta to discuss a gift because the Gemara holds that this is only for a gift (but in a sale, the money determines how much was sold).
iii.Tosfos (92a DH v'Lichzi): Even Chachamim say that the money does not determine how much was sold only when this opposes a majority and a Chazakah.
iv.Beis Yosef (DH v'Zeh Lashon Nimukei, citing the Ritva): The Tosefta discusses a sale, i.e. when the price does not reveal how much he sold, e.g. he said that three experts assess it and set the price..
v.Note: We could also say that it was sold together with something without a precise market price, e.g. a city, land of extraordinarily high or low quality, something sometimes sold for three and sometimes for four, or one who sells at a discount for he needs money immediately.