Gemara

If one was Maktir (the entire Kometz,) the volume of a sesame seed at a time, each time with intent to eat (Chutz li'Zmano) the volume of (another) sesame seed (in all, a k'Zayis), Rav Chisda, Rav Hamnuna and Rav Sheshes argued. One said that it is Pigul, one said that it is Pasul, and one said that it is Kosher.

The opinion that says Pigul holds that piecemeal eating (the volume of a sesame seed at a time) is considered eating, and piecemeal Haktarah is considered Haktarah. (Therefore, it is a genuine intent of Pigul);

The opinion that says Pasul holds that piecemeal eating is (not - some texts deletes this word) considered eating, and piecemeal Haktarah is not considered Haktarah (to make Pigul or to be Machshir the Korban;

The opinion that says Kosher holds that piecemeal eating is not considered eating, but piecemeal Haktarah is considered Haktarah. (Therefore, it is a Kosher Haktarah.)

Kerisus 12b (Mishnah - R. Meir): Even if one delays while eating an Isur like one who eats crumbs, he is liable;

(Chachamim): He is liable only if the delay from beginning to end was bi'Chdei Achilas Pras (within the time needed to eat half a standard loaf.

Pesachim 114b (Beraisa): If one ate (Maror) half at a time, he was Yotzei, as long as he did not delay Kdei Achilas Pras between one eating and another

Sukah 42b: If a child can eat a k'Zayis of grain, we must distance (Divrei Kedushah) four Amos from his excrement and urine.

(Rav Chisda): This is if he can eat it within Kdei Achilas Pras.

Rishonim

Rambam (Hilchos Pesulei ha'Mukdashim 16:9): If one was Maktir the volume of a sesame seed of the Kometz with the Levonah, and intended to eat tomorrow the volume of a sesame seed of the Shirayim, until he finished offering the Kometz and Levonah with intent Chutz li'Zmano, it is Pasul, but not Pigul. Even though it is normal to eat piecemeal, it is not normal to be Maktir piecemeal. It is as if the Kometz was not Huktar.

Birkas ha'Zevach (16b Chidushim): The text says 'the opinion that says Pasul holds that it is normal to eat piecemeal, but it is not normal to be Maktir piecemeal.' This is the text of the Shitah Mekubetzes and the Rambam.

Sefas Emes (16b DH u'Man): This opinion holds that it is not normal to eat piecemeal, but it is not normal to be Maktir piecemeal. Why did Birkas ha'Zevach delete 'not' from the text? This forces us to say that Amora'im have totally opposite reasoning! (The one who says 'Kosher' holds that piecemeal Haktarah is more normal than piecemeal eating.) However, the Rambam wrote like Birkas ha'Zevach says. This requires investigation, for it is not normal to eat piecemeal!

Rambam (Hilchos Chametz 1:7): It is forbidden to eat any amount of Chametz during Pesach, for it says "Lo Yochal Chametz". One is Chayav Kares or Korban only for a Shi'ur, i.e. a k'Zayis. One who eats less than a k'Zayis is lashed mid'Rabanan.

Kesef Mishneh: Why did the Rambam require a verse? In the entire Torah, Chetzi Shi'ur is forbidden! The verse connotes oppositely, that only a Shi'ur of Achilah is forbidden! Why does the Rambam discuss less than a k'Zayis? He was discussing one who eats any amount! I say that it is because he initially said 'any amount', which connotes that even the tiniest amount for which there is no Hana'ah. The Rambam concludes to teach that even though even the tiniest amount is forbidden, there are lashes only for an amount that his throat gets some benefit from it, i.e. an amount proper to call 'less than a k'Zayis.' However, it is not clear what is the source to distinguish like this.

Mishneh Halachos (13:86 DH u'Ketzas): I say that the Rambam learned from Menachos. Each Amora could be like all opinions, including the one who said that piecemeal Haktarah is not normal. R. Yochanan (26b) holds that Haktarah of less than a k'Zayis is Haktarah. This shows that piecemeal is worse than less than a k'Zayis. The Rambam rules like the opinion that piecemeal Haktarah (i.e. like sesame) is not Haktarah, but such piecemeal eating is eating.

Rambam (Hilchos Ma'achalos Asuros 14:8): If one ate the size of a barley seed or mustard seed of any Asur food, paused, and ate another drop, until he finished a k'Zayis, whether he was Shogeg or Mezid, if he delayed the time to eat three eggs he is Chayav Kares or lashes or Korban, as if he ate at once. If he delayed longer than this, even if he did not pause, rather, he ate a bit at a time, it does not join and he is exempt.

Rashi (Sukah 42b DH v'Hu): If one delays longer than Kdei Achilas Pras, it is as if he ate half a k'Zayis today and half a k'Zayis tomorrow. A tradition from Moshe from Sinai teaches that eating does not join over a period longer than this.

Terumas ha'Deshen (139): The ideal Mitzvah is to swallow the entire k'Zayis of Matzah or Maror when it is mashed, at once. The Mordechai (Pesachim 61asked how he (Hillel) could eat a k'Zayis of Matzah and a k'Zayis of Maror and a k'Zayis of Charoses (this should say 'Pesach) together? One cannot swallow three k'Zeisim at once! The question shows that one should not swallow it bit by bit. Rather, he should swallow it all at once. Likewise, we should swallow the entire k'Zayis of Matzah or Maror at once.

Poskim

Shulchan Aruch (OC 208:9): If one mixed millet flour with grain flour and made bread from it, he blesses Birkas ha'Mazon afterwards only if he eats a k'Zayis of the grain flour in Kdei Achilas Pras.

Magen Avraham (15): For all Isurim, one is liable only if he ate k'Zayis in Kdei Achilas Pras. The same applies to Birkas ha'Mazon.

Gra (DH uliv'Sof): Every Berachah Acharonah requires k'Zayis in Kdei Achilas Pras.

Shulchan Aruch (210:1): One who eats less than a k'Zayis or drinks less than a Revi'is of wine or other drinks blesses beforehand, but not afterwards.

Magen Avraham (1): If one a little, and later ate a little, if he waited more than Kdei Achilas Pras, they do not join, like we say about Yom Kipur (OC 612:3, Yoma 80b). Rashi says that we require a k'Zayis for a Berachah Acharonah because it says 'Achilah', which is a k'Zayis. If one delayed Kdei Achilas Pras, this is not called eating. This applies to all Isurim. Olas Tamid (207, citing Shirei Keneses ha'Gedolah) distinguishes Yom Kipur from Birkas ha'Mazon. He obligates Birkas ha'Mazon even if he delayed more than Kdei Achilas Pras. I disagree. If one ate less than a Shi'ur, went outside and returned, he needs a new Berachah Rishonah. It is not clear whether the eatings join for (Birkas ha'Mazon). It seems that they join.

Olas Tamid (brought in Machatzis ha'Shekel DH Lechalek): Yom Kipur depends on what settles one's mind. Eating (the volume of a date) in more than Kdei Achilas Pras does not settle one's mind. Berachah Acharonah depends on benefit. Since his palate benefited from a Revi'is or k'Zayis, it joins even over more than Kdei Achilas Pras. In practice, this requires investigation.

Machatzis ha'Shekel (DH d'Ha): Isurim do not depend on what settles one's mind. Even so, one is exempt for eating in more than Kdei Achilas Pras, for it is not called eating. The same applies to Birkas ha'Mazon, for the verse mentions Achilah.

Eshel Avraham (DH u'Mah she'Chosav Al): Also Pri Chodosh (Teshuvah says that Isurim eaten in more than Kdei Achilas Pras do not join, but foods join even in more than Kdei Achilas Pras, for he blesses due to the benefit his innards received. However, if he ate to satiation, the Torah obligates Birkas ha'Mazon even if he ate very slowly ("v'Achalta v'Savata u'Verachta" - you will eat, be satiated, and bless). Only if he ate only a k'Zayis, and he blesses Birkas ha'Mazon due to "v'Achalta", it does not join (for this is not called eating). This requires investigation.

Sha'ar ha'Tziyon (10): This is not so clear. Perhaps even though there is enough for satiation, we require also v'Achalta, and this is not called eating, like the Magen Avraham said. Perhaps this is why Eshel Avraham concluded 'this requires investigation.' If one was satiated, and ate a k'Zayis at once, (even if he ate the rest very slowly), in any case he must bless Birkas ha'Mazon.

Kaf ha'Chayim (7): It seems that also Rashi (Sukah 42b) holds that eating does not join over more than Kdei Achilas Pras also regarding Berachos. Since Poskim disagree, one should not eat slowly and enter a Safek. If he did, he should eat a k'Zayis at once, and his Birkas ha'Mazon will exempt also what he ate beforehand. If he cannot eat a k'Zayis, he only thinks Birkas ha'Mazon.

Mishbetzos Zahav (DH bi'Shtei): In Kerisus (13a) we say that a baby that nursed from a Tamei Mes woman is Tahor. It is a Safek whether he nursed a Shi'ur (to be Metamei him), and even if he did, perhaps he did not nurse within Kdei Achilas Pras, even though it is normal (for a baby to nurse slowly).

Mishnah Berurah (1): If one paused in the middle of drinking, some say that the two times do not join. Some say that they join up to Kdei Achilas Pras. It is normal to drink hot tea or coffee, and it is hard to drink it like other drinks, without stopping. Opinions differ about whether one should say a Berachah Acharonah. The custom is not to bless. Meticulous people let a Revi'is cool off, so they can drink it without pausing. It is good to do so, to fulfill all opinions, especially since the Gra holds that up to Kdei Achilas Pras joins.

Kaf ha'Chayim (190:18): To make a Berachah Acharonah, one must drink a Revi'is in the normal time, like the law of Yom Kipur. L'Chatchilah, one should not pause in order that he can bless afterwards. If he paused, he should try to drink another Revi'is without pausing, or (if the Berachah Acharonah is Borei Nefashos) eat a food obligating him to say Borei Nefashos. If he cannot, he only thinks the Berachah, for it is a Safek.

Shulchan Aruch (475:6): If one ate a half-k'Zayis (of Matzah), then ate another half-k'Zayis, he was Yotzei, as long as he did not delay between one eating and another Kdei Achilas Pras. (See OC 612:3).

Magen Avraham (15): Really, it means that he did not delay from the beginning to the end Kdei Achilas Pras, like it says in OC 612.

Birkei Yosef (475:5): Chak Yosef says that the Shulchan Aruch is precise. Regarding Yom Kipur, Chachamim knew that a date settles the mind, but less does not. Therefore, it must be eaten within the time (to be liable). Here, if there is less than Kdei Achilas Pras between one eating and another, it is like one eating, so he was Yotzei. This is wrong. Regarding Isurim, the Rambam exempts one who did not eat a Shi'ur within Kdei Achilas Pras. A Mishnah in Kerisus explicitly says so. The Shulchan Aruch merely cites the Beraisa in Pesachim. If he held that there were a difference between here and Yom Kipur, he would have said so,

Mishnah Berurah (40): Likewise, if he did not pause, but he ate very slowly and delayed Kdei Achilas Pras, it does not join and he was not Yotzei.

Mishnah Berurah (41): Within Kdei Achilas Pras he was Yotzei b'Di'eved. L'Chatchilah one must eat a k'Zayis at once and swallow it.

Shulchan Aruch (612:3): If one ate, and later ate more, if there is from the beginning to the end (at most) Kdei Achilas Pras, they join (to the Shi'ur of a large date to be liable for Yom Kipur). If not, they do not join.

Kaf ha'Chayim (16): This is if he paused Stam. If he paused in order to uproot the Torah Isur, it joins.