Gemara

Mishnah: Afikoman is forbidden after eating Korban Pesach.

Rav: This teaches that one may not clear his Kelim to another Chaburah. (One may not eat anything in another Chaburah, lest he eat Pesach there.)

Shmuel: It forbids dessert such as Ordilai (mushrooms) or chicks.

R. Chanina bar Shila and R. Yochanan: It forbids dessert such as dates, parched grain and nuts.

A Beraisa supports R. Yochanan.

Rashbam: The Beraisa also supports Shmuel. Shmuel and R. Yochanan do not argue, each lists desserts common in his locale.

Rebuttal (Ran on Rif, DH Gemara): All the Amora'im decree lest one eat Pesach in two places. Shmuel forbids eating meat after Pesach even in the same place, lest one confuse the types of meat and forget that he ate Pesach, and come to eat elsewhere (Ordilai are fowl). The Beraisa is like R. Yochanan, who forbids eating anything after Pesach.

Version #1 (Shmuel): (Nowadays, we eat Matzah at the end to commemorate the Pesach, which was eaten at the end, with Matzah (according to Hillel).) We may not eat after this Matzah.

Question (Mishnah): We may not have Afikoman after Pesach.

Inference: Afikoman is forbidden after Pesach, but it is permitted after Matzah.

Answer: No, the Mishnah teaches a bigger Chidush. Matzah's taste is not so strong, so we may not eat after it (for then the taste of Matzah would not remain in our mouths). But Pesach's taste is strong, we would have thought that one may eat after it, for its taste would remain in our mouths! The Mishnah teaches that this is not so.

Support (Beraisa): One may fill his stomach with the following (on Pesach night) as long as he eats a k'Zayis of (proper) Matzah at the end (these are not "Lechem Oni") - spongy Matzah, Matzah fried in honey and oil, and wafers made from a thin dough.

Inference: One must eat Matzah at the end, but if one ate Matzah (for the Mitzvah) at the beginning, he may not eat (these or anything else) afterwards!

Rejection: No, the Beraisa teaches a bigger Chidush. Had it permitted invalid Matzah after eating valid Matzah with appetite, one might have thought that he may not eat invalid Matzah first, lest eating Matzas Mitzvah will be Achilah Gasah (gorging himself)! Therefore the Beraisa permits even to eat invalid Matzah first.

Version #2 - Mar Zutra - Shmuel: We may have Afikoman after Matzah.

Support (Mishnah): We may not have Afikoman after Pesach.

Inference: It is forbidden after Pesach, but it is permitted after Matzah.

Rejection: No, the Mishnah teaches a bigger Chidush. Dessert is forbidden not only after Matzah, whose taste is not strong; rather, it is forbidden even after Pesach, whose taste is strong!

Question (Beraisa): One may fill his stomach with spongy Matzah, Matzah fried in honey and oil, and wafers made from a thin dough, as long he eats a k'Zayis of Matzah at the end.

Inference: One must eat Matzah at the end; but if one ate Matzah at the beginning, he may not eat afterwards!

Answer: No, the Beraisa teaches a bigger Chidush. Had it permitted eating these after Matzah, one might have thought that he may not eat them first, lest he eat Matzah Achilah Gasah - the Beraisa permits even to eat them first.

120b - Rava: Nowadays, according to R. Elazar, if someone ate Matzah after midnight, he was not Yotzei.

Objection: This is obvious - since Matzah is equated to Pesach, it is like Pesach!

Answer: One might have thought that the Torah uprooted it from the Hekesh (by commanding to eat Matzah even when there is no Pesach)- Rava teaches that this is not so, rather, the Mitzvah to eat Matzah nowadays is like when there is Pesach.

Rishonim

Rif and Rosh (10:34): Presumably, the Halachah follows Version #1, for it is the Stam Gemara, whereas Version #2 is the opinion of an individual. This is our custom. After eating delicacies and fruits, one eats a k'Zayis of Matzah Shmurah (guarded) for the Mitzvah, and nothing else afterwards except for the cups of Birkas ha'Mazon and Hallel.

Rif (Daf 26a) and Rosh (10:33) - Beraisa - R. Tarfon: One says Hallel ha'Gadol over the fifth cup; some say, "Hash-m Ro'i Lo Echsar..."

Note: Our text, and that of Tosfos (117b Revi'i) and the Rashbam (118a Hachi Garsinan) do not mention a fifth cup.

Rif: If one is thirsty, he may drink water, but not wine.

Rebuttal (Rosh 10:33): There is no source to forbid drinking after Pesach (or Matzah). Afikoman is forbidden afterwards, i.e. food! The Yerushalmi forbids drinking between the third and fourth cups lest one get drunk. It is not concerned for losing the taste of Pesach! Our custom is not to drink extra wine afterwards. This is because we are commanded to spend the entire night discussing Hilchos Pesach and Yetzi'as Miztrayim until one is overcome by sleep; wine inebriates people.

Rif: If one has only one k'Zayis of Shmurah Matzah, he blesses ha'Motzi on other Matzah, and at the end he blesses Al Achilas Matzah on the Shmurah Matzah. He then blesses Al Achilas Maror and eats Maror, and then eats Korech without a Berachah.

Source: We learn from the Beraisa which permits eating spongy Matzah, Matzah fried in honey and oil, and wafers made from a thin dough, as long he eats a k'Zayis of Matzah at the end.

Rambam (Hilchos Chametz u'Matzah 8:9): After eating Matzah, Maror and Korech, one eats and drinks whatever he wants. At the end he eats Korban Pesach; even a k'Zayis suffices. He does not taste anything afterwards. Nowadays he eats a k'Zayis of Matzah at the end and he does not taste anything afterwards. This is so that he taste of the Pesach or Matzah, which it is a Mitzvah to eat, will be in his mouth at the end of his meal.

Rashbam, brought in Rosh (10:34): One must eat Matzah at the end of the meal to commemorate the Matzah eaten wrapped with the Pesach. This is the Matzah that was broken earlier; it is eaten now for the Mitzvah. Really, we should bless Al Achilas Matzah at the end. However, Rav Chisda taught that it is unreasonable to bless Al Achilas Maror after he already ate it, and the same applies to Matzah. After eating this Matzah we do not eat anything else, lest the taste of Matzah not remain in our mouths.

Rosh (ibid.): According to the Rashbam, the Matzah at the end must be eaten with Maror and (dipped in) Charoses, just like the Matzah eaten with the Pesach. Even Chachamim who argue with Hillel agree that the Mitzvah is to eat them together (i.e. one after the other - Hagahos ha'Bach).

Rebuttal (Rosh ibid.): According to the Rashbam, why do we eat Korech earlier (right after Maror)? The Korech at the end should suffice!

Rosh (ibid.): Rather, we fulfill the Mitzvah with Korech earlier; we eat Matzah at the end to commemorate the Pesach. Therefore, we do not eat after it, like Pesach. It need not be eaten with Maror and Charoses.

Poskim

Shulchan Aruch (OC 478:1): One may not eat anything after the Afikoman.

Beis Yosef (DH Acher): Nowadays we call the Matzah eaten at the end 'Afikoman' because we hold like Version #1 of Shmuel, which forbids eating after it.

Mishnah Berurah (1): If one ate afterwards, he should eat another k'Zayis of Matzah Shmurah for Afikoman (if he did not yet say Birkas ha'Mazon - Kaf ha'Chayim (2)).

Rema: Also, it may not be eaten in two places; we find that one who slept may not eat again for this is like eating in two places.

Beis Yosef (DH u'Mah she'Chosav): Shmuel and R. Yochanan argue with Rav regarding dessert, but all forbid eating in two places.

Tur: Nowadays Matzah is like Pesach regarding both of these laws.

Rebuttal (Tosfos 119b DH Amar): Rav cannot say that Matzah nowadays is like Pesach regarding eating in two places. The Mishnah forbids this regarding Pesach; it would have been a bigger Chidush to teach this regarding Matzah! Regarding dessert, we answered that it is a bigger Chidush to forbid regarding Pesach, but this does not apply to eating in two places!

Magen Avraham (2): One should not even eat the Afikoman at two tables in the same room, like we find (in the Mishnah regarding Korban Pesach) on 86a. The rest of the meal may be eaten in two places.

Shulchan Aruch (481:1): One may not drink wine after the four cups, only water.

Rema: All beverages are forbidden like wine.

Mishnah Berurah (2): Some Poskim forbid drinking lest one get drunk and fail to discuss Hilchos Pesach and Yetzi'as Miztrayim afterwards. They permit beverages that do not intoxicate. Others forbid because it looks like he adds to the enactment of four cups. They forbid any Chemar Medinah. Others forbid because it is Mevatel the taste of Matzah. They forbid all drinks, just like food. Presumably, the Mechaber and Rema are stringent for all the reasons, for they did not specify the reason. Nevertheless, drinks like tea with a faint taste are permitted. L'Chatchilah one should be stringent like this last opinion; if there is a big need, one may be lenient to drink anything that does not intoxicate; in any case this is permitted at the second Seder in Chutz la'Aretz.

Rema: If a fastidious person is very thirsty, he make drink a fifth cup and say Hallel ha'Gadol over it.

Kaf ha'Chayim (6,8): This is permitted only if he did not yet say Hallel ha'Gadol. The Mechaber did not mention a fifth cup because he is concerned for the opinions that forbid it.

Avnei Nezer (OC 381:5): Surely, the obligation that the taste of Pesach remain in our mouths is only during the time of the Mitzvah; the same applies to the Afikoman. I.e., the opinion that requires eating it before midnight allows to eat again after midnight. One may eat a k'Zayis of Matzah before midnight on condition that if the Halachah follows this opinion, this is the Afikoman, and he may continue to eat after midnight. To fulfill the other opinion, at the end of his meal he should eat another k'Zayis on condition that if the Halachah follows the opinion that the Mitzvah applies the entire night, this is the Afikoman.