Gemara

33b (Rav Acha bar Rav Avya citing R. Yochanan): If grapes became Tamei, one may stomp less than k'Beitzah [at a time], and the wine is Tahor even for Kodshim.

Inference: He holds that juice inside a fruit is 'deposited'. It is not Mekabel Tum'ah until it leaves. At that time, there is not a Shi'ur.

Question: If so, it should be Tahor even if he stomps exactly k'Beitzah!

(Mishnah): If a Tamei Mes squeezed exactly k'Beitzah of olives or grapes, they are Tehorim.

Answer: That is b'Di'eved. L'Chatchilah, one may not do so, lest he stomp more than k'Beitzah.

44a - Question (Abaye - Mishnah): If a porridge was Chulin and the garlic and oil were Terumah; and a Tevul Yom touched part [of the Terumah], he is Metamei only the place he touched.

Question: The Terumah should be Batel in the majority (Chulin. A Tevul Yom is not Metamei Chulin!)

Answer (Rabah bar bar Chanah): [The Terumah is not Batel] because a Zar is lashed [mid'Oraisa] for eating a k'Zayis [of the mixture].

Shabbos 14a (Mishnah): [Stam] hands [disqualify Terumah].

This was decreed because hands touch many things.

91a: The Shi'ur for Kabalas Tum'ah [for food] is k'Beitzah.

Sukah 26b (Mishnah): Once, they brought to R. Tzadok less than k'Beitzah to eat. He wrapped it in a cloth and ate it outside the Sukah, and did not bless afterwards.

27a - Inference: Had it been k'Beitzah, he would have needed to eat it in the Sukah.

Rejection: No. A k'Beitzah would have obligated Netilas Yadayim and a Berachah Acharonah.

Berachos 49b: R. Meir obligates returning (to burn Chametz or Kodesh meat) for a quantity that is important enough to be Metamei, i.e. a k'Beitzah;

Taharos 2:1 (Mishnah): If a woman touched a wet leaf outside a pot of vegetables less than k'Beitzah, it is Tamei and the rest of the pot is Tahor.

Rishonim

Roke'ach (328): If one eats less than a k'Beitzah [of bread], he washes due to Safek, and does not bless.

Beis Yosef (OC 158 DH Kasav): It seems that since less than k'Beitzah is not Mekabel Tum'as Ochlim, perhaps Chachamim did not obligate Netilas Yadayim. Or, perhaps they obligated Stam one who eats bread, and did not distinguish less than k'Beitzah from more than k'Beitzah. Therefore, he washes without a Berachah.

Tosfos (91a DH Iy): Our Gemara connotes that less than k'Beitzah is not Mekabel Tum'as Ochlim. Rashi brought from Toras Kohanim that any amount is Mekabel Tum'as Ochlim, but only k'Beitzah is Metamei others. R. Tam says that this is an Asmachta. Toras Kohanim also includes Ma'aser of Yerek, which is only an Asmachta. If a Tamei Mes squeezed exactly k'Beitzah of olives or grapes that were not Huchshar, they are Tehorim. They are Huchshar only after a drop exudes, and then they are less than k'Beitzah. Rashi can say that even though any amount is Mekabel Tum'ah, k'Beitzah is required to receive Hechsher. R. Pores says so in his name (Shabbos 145a). He learns from "Asher Ye'achel." R. Tam proved from Pesachim 44a that less than k'Beitzah is not Mekabel Tum'as Ochlim. Rashi changed the text to say that the oil and garlic is Batel to the majority. There was no need to change the text. Also, we cannot say that they are Batel to be lenient! Also, what is intact is not Batel. Since we say that he is Metamei only what he touched, this implies that they are intact! (Rather, the text says 'why is the place he touched Pasul?') In Kerisus (21a) Rashi retracted. Chulin 24b says that the Torah declared that the contents of a Kli Cheres are Tamei, even if it is full of mustard seeds [even though the interior seeds are separated by many layers of seeds from the Kli]. It does not literally discuss mustard seeds [for they are too small to be Mekabel Tum'as Ochlim]. Rather, it refers to eggs. It mentioned mustard because there are many layers, and it is Mekabel Tum'ah mid'Rabanan.

Tosfos Yom Tov (Taharos 2:1 DH Ein): A leaf less than a k'Beitzah becomes Tamei. This is like Toras Kohanim, which the Rambam brought above (Mishnah 1:2), which expounds that food of any size can become Tamei, but it is not Metamei others. The Bartenura explained like this in Mishnah 10:5 and Eduyos 2:5. However, in Mishnah 1:1 and elsewhere, he explains that k'Beitzah is the Shi'ur of Kabalas Tum'ah! In Ohalos 13:5, the Bartenura and R. Shimshon said that this is the Shi'ur mid'Oraisa. The Rambam agrees. The Toras Kohanim is an Asmachta. This is an old argument, like Tosfos in Shabbos says. Wherever the Bartenura said that less than k'Beitzah is not Mekabel Tum'as Ochlim, we must say that there Chachamim chose not to be stringent. They said [to be stringent], and they said [where not to be stringent].

Rashi (Shabbos 14a DH Askaniyos): Hands touch the skin and filthy places. If they would touch Terumah, this is disgraceful and this could make it repulsive. My Rebbeyim say that we are concerned lest the hands touched Tum'ah. This is difficult. If they touched an Av ha'Tum'ah, the person is a Rishon l'Tum'ah [and he is Metamei food even after he washes his hands]! Also, if so the decree should be on his entire body!

Tosfos (26b DH Natlo) and Ran (Sukah 11b DH ucheshe'Nasnu): Rashi says that R. Tzadok took the food in a cloth for cleanliness. There was no need to say so. R. Tzadok was a Kohen. He ate everything in Taharah as if it were Terumah. Hands [that were not washed and guarded] are a Sheni l'Tum'ah, and they disqualify Terumah. Even less than k'Beitzah is Mekabel Tum'ah, like it says in Taharos 2:1.

Eshel Avraham (OC 158:3): Taharos 2:1 proves that less than k'Beitzah is Mekabel Tum'ah. The question is whether this is mid'Oraisa or mid'Rabanan. If it is only mid'Rabanan, it is reasonable that Chachamim did not decree [to wash] on all of Yisrael due to a minority (Kohanim), without a support from the Torah. (The Torah is Metamei only k'Beitzah.) Rashi says that we are concerned for sullying Terumah. Surely this applies to any amount. It is not a decree on a decree to obligate Yisrael to wash for any amount of Chulin. (Rather, it is a single decree.) This is why Rashi said in Sukah that he used a cloth for cleanliness. R. Tzadok was given total Chulin, so there was no concern lest his hands be Metamei it. Tosfos is difficult. If it were Chulin Al Taharas Terumah, even for k'Beitzah a cloth suffices for Kohanim! Tosfos himself (27a DH Ha) asked this and could not answer. The Roke'ach was unsure whether we follow Rashi in Sukah (R. Tzadok used a cloth because he was finicky), or Tosfos, or Rashi in Shabbos.

Poskim

Shulchan Aruch (OC 158:2): Some say that if one eats less than a k'Beitzah [of bread], he washes without a Berachah.

Magen Avraham (3): Tosfos and the Ran disagree with this. See Tosfos in Pesachim.

Gra (DH Yesh): Also in Chulin 107a, the Gemara wanted to infer that one must wash for k'Beitzah. However, perhaps R. Tzadok holds like R. Yehudah, who obligates blessing after k'Beitzah [of bread], and similarly regarding washing. However, we rule like R. Meir [that one blesses after a k'Zayis], and similarly regarding washing. Or, R. Meir could agree that since less than k'Beitzah is not Metamei, one need not wash for it, even though it is Mekabel Tum'ah mid'Rabanan. The Magen Avraham says that the Shulchan Aruch is unlike Tosfos and the Ran. I disagree. Surely one must wash for any amount of Terumah, since [Stam] hands disqualify it! R. Shimshon brings from a Tosefta that Taharos 2:1 discusses Stam hands. However, one need not wash. A cloth suffices. For Chulin, one does not need even a cloth.

Mishnah Berurah (9): Since less than k'Beitzah is not Mekabel Tum'ah mid'Oraisa, Chachamim did not decree Netilas Yadayim for it. Or, since regarding Birkas ha'Mazon a k'Zayis is considered eating, Chachamim similarly enacted Netilas Yadayim for it. Therefore, one washes without a Berachah, since the Berachah is not Me'akev. One blesses Al Netilas Yadayim even for the volume of an egg without the shell.

Kaf ha'Chayim (8): This is because k'Beitzah without the shell is Mekabel Tum'ah (Rambam Hilchos Tum'as Ochlim 4:1). It is proper to eat [at least] this amount to avoid the Safek about the Berachah.