Gemara

(Beraisa - R. Eliezer): If one made cheese k'Grogeres (the volume of a fig) on Shabbos b'Shogeg, he is Chayav Chatas. If he did so on Yom Tov b'Mezid, he gets 40 lashes.

Shabbos 105b (Mishnah): If one tore out of anger or due to his Mes, or did anything destructive, he is exempt.

111a (Rav Simi bar Chiya citing Rav): One may not wrap a rag tightly in the spout of a barrel on Yom Tov [even though he does not intend to squeeze out liquid].

Abaye and Rava both say that R. Shimon agrees about a Pesik Reishei!

Tosefta (Shabbos 12:7): Erasing is liable only in order to write. Erasing in order to fix any amount is liable.

Rishonim

Rambam (Hilchos Shabbos 7:6): If one takes milk and puts [the contents of a nursing animal's] stomach inside to curdle it, he is liable for a Toladah of Borer, for he separated the whey from the milk. Similarly, every Av Melachah has Toldos like this.

Rambam (8:15): One who grinds k'Grogeres is liable. Similarly, one who minces spices and ingredients in a mortar is liable for grinding. Cutting to size detached Yerek is a Toladah of grinding, or sawing wood in order to benefit from the sawdust [is liable for any amount]. One who cuts wood is not liable until he cuts enough to cook k'Grogeres of an egg.

Rambam (16): One who kneads k'Grogeres is liable. Kneading earth is a Toladah of kneading. The Shi'ur is to make an opening for an oven of gold smelters.

Rambam (10:13): One who makes cheese is liable for a Toladah of Boneh (building). He is liable only for a k'Grogeres.

Ran (Shabbos 41a DH u'Lefichach): One may not wrap a rag tightly in a spout. Such squeezing is not an Av Melachah. It is only a Toladah, like Mefarek (extracting), which is a Toladah of Dash (threshing). Surely it is like Dash only when he needs the liquid squeezed out! Why is he liable when he does not need it? One may squeeze pickled vegetables for the sake of the vegetables (145a)! One may not walk through water, or bring a towel with which he dried himself, lest he come to squeeze out water. Some forbid immersing Kelim on Yom Tov due to squeezing. R. Tam explained that such squeezing is a Toladah of Melaben (laundering). Another squeezing is a Toladah of Dash, but only if he needs the liquid squeezed out.

Tosfos (105b DH Ha): If one who tore due to a Mes was Yotzei Keri'ah, tearing was Melachah she'Tzerichah l'Gufah, for he needs the Mitzvah. All agree that one who tore for a Mes over which he need not tear is exempt, for this is Mekalkel (destructive). The Gemara connotes that R. Shimon does not considered Tikun Mitzvah to be Tikun. He learns from Bris Milah and burning a Bas Kohen (Misas Beis Din) that for wounding and burning, one is liable for Mekalkel. If one is liable for Tikun Mitzvah, how can he learn to obligate Mekalkel? There, it is totally Mekalkel, other than the need of the Mitzvah. Tearing is a Tikun in the garment. It permits the Avel to wear it at all times (even during the Shivah), and it gives outlet to his anger. Also, the Tikun is while tearing, so it is not considered Mekalkel. There, the Tikun is at the end. There is no Mitzvah while wounding or burning. It is only Hechsher (what is needed for the sake of a) Mitzvah, until it is completed.

Poskim

Maharalbach (23): The Rambam always teaches which Av the Toladah is from, for three reasons. 1) If one did an Av and its Toladah in one Helam (forgetting), he is liable only one Korban. 2) The Shi'ur for the Toladah is like the Shi'ur for the Av, unless there is a clear reason why it is different. 3) If one was warned for an Av, this is valid warning. The Rambam holds that it suffices to warn 'you will be Chayav Misah if you do this.' However, warning for the wrong Av is invalid.

Be'er Yitzchak (OC 13:5): If we find only that a Toladah was permitted for Ochel Nefesh on Yom Tov, we do not say mi'Toch that the Toladah is permitted for needs of Ochel Nefesh, the Av is permitted even not for needs of Ochel Nefesh. Since the Av is more important than the Toladah, it is not drawn after the Toladah. Perhaps only what is not important was permitted. What was important in the Mishkan is called an Av (Shabbos 96b). Regarding Shevi'is, the Torah forbids only Avos (Mo'ed Katan 3a). 'V'Asah me'Achas me'Henah" teaches liability for Toldos of Shabbos, i.e. to be stringent about the Toladah like the Av. We have no source to be lenient about the Av due to the Toladah. It is more reasonable to say that the Av is forbidden on Yom Tov without the Toladah, like Shevi'is. Therefore, even though making cheese, which is a Toladah of Boneh, is permitted on Yom Tov, this does not permit the Av of Boneh, which is more stringent.

Note: The Gemara says that one is liable for making cheese on Yom Tov! Perhaps this is when it is not needed for Ochel Nefesh. The Magen Avraham and Mishnah Berurah (510:11 and 21) forbid [only] due to Uvda d'Chol (a weekday action), for it is normally done for many days at once [but mid'Oraisa it is permitted, i.e. if needed for Ochel Nefesh - PF].

Be'er Yitzchak: The Gemara (96b) did not list this among differences between Avos and Toldos, for there it discusses only Shabbos. The Rambam proved this from Shevu'os 15b, which says that Binyan Beis ha'Mikdash does not override Yom Tov, without any distinction. The Ran (Beitzah 12b) asked why we may mince spices on Yom Tov, according to the opinion that the Torah forbids grinding. Mincing is a Toladah of grinding! The Pnei Yehoshua answered that we forbid only things like reaping and grinding, which are normally done for many days at once. Normally, people mince spices only for the pot they cook now. We do not say that since the Torah permits mincing, we permit the Av (grinding)!

Bi'ur Halachah (340:14 DH v'Chayav): The Rambam (8:15) holds that one who saws wood to benefit from the sawdust is liable for any amount, even though this is a Toladah of grinding and the Shi'ur for grinding is k'Grogeres. This shows that the Shi'ur for the Toladah need not be the same as the Shi'ur for the Av. However, gluing is liable due to sewing. We do not find a distinction between [the Shi'ur for] sewing leather and other garments. The same applies to gluing. The Shulchan Aruch connotes that paper is similar. What is the law regarding separating, which is due to Kore'a? Even if it is not in order to sew, if it is for any Tikun, it is as if it is in order to sew. Or, if one tears out of anger [for which the Rambam is Mechayev], is the Shi'ur in order to sew two stitches? Or, perhaps this Shi'ur is only when he intends to sew them! One who tears for a Mes is liable for a Tefach. If he tore less than a Tefach, he did not fulfill the Mitzvah. (This is like Tosfos 105b DH Ha. The Rambam obligates for calming his anger. It is not clear whether this requires a Tefach.) Perhaps one who intends for a different Tikun is liable for what gives the Tikun, whether this is a stringency or leniency. The Mishnah says that if one is Mekalkel for the sake of Tikun, the Shi'ur is like for the Tikun. This is when there is a known Shi'ur for the Tikun, e.g. erasing need to write, or tearing in order to sew. The Shi'ur is based on what is needed for Tikun. It does not depend on two stitches. This requires investigation.

Aruch ha'Shulchan (OC 321:17): The Shi'ur for human food is k'Grogeres. The Shi'ur for kneading earth is like the Shi'ur for Hotza'ah (taking it to Reshus ha'Rabim).

Har Tzvi (Tal Harim, Gozez 1): The Magen Avraham (Reish Siman 340) permits telling a Nochri to cut a Yisrael's fingernails, for it is Melachah she'Einah Tzerichah l'Gufah. The Rambam obligates for this! The questioner learned from the Ran that the Rambam obligates for Melachah she'Einah Tzerichah l'Gufah only for Avos, but not for Toldos. All agree that we do not learn this from the Av, so it is not a Toladah. The Ran wrote "this squeezing is not an Av Melachah. It is only a Toladah, like Mefarek (extracting), which is a Toladah of Dash (threshing). Surely it is like Dash only when he needs the liquid squeezed out! Why is he liable when he does not need it?"

Note: Even though the Ran exempts Melachah she'Einah Tzerichah l'Gufah, surely he teaches that here all exempt. If not, he did not need to say that this squeezing is only a Toladah!

Har Tzvi (DH Hinei): Gilyon ha'Shas on the Yerushalmi (Shabbos 48a) understood the Ran to say that even R. Yehudah obligates Melachah she'Einah Tzerichah l'Gufah only regarding Avos, but not for Toldos.

Hagahah: Iglei Tal (Dash 84) said that there is no reason to distinguish. He observed that in the first Perek of Bava Kama, we did not say that this is a difference between Avos and Toldos.

Har Tzvi: Why don't we learn from the Av to be liable for this? Perhaps Melachah she'Einah Tzerichah l'Gufah is like a Toladah. (Tosfos Mo'ed Katan 2b DH v'Tzarich connotes like this). We do not find a Toladah of a Toladah.

Hagahah: Avnei Nezer (OC 96:5) said that someone wanted to prove that stomping grapes is an Av, for one is liable for squeezing grapes, which is a Toladah, and one cannot be liable for a Toladah of a Toladah. However, R. Chananel (Shabbos 73b) explicitly says that grafting and Mavrich (inserting shoots into the ground) are Toldos of Note'a, which is a Toladah of Zore'a.

Yabi'a Omer (5 OC 31 DH Bereishis): Why is the Rambam Mechayev for wounding a person due to Mefarek, a Toladah of Dash? Dash applies only to Gidulei Karka! His son (Birkas Avraham, 18) answered that the Av Melachah applies only to Gidulei Karka, but its Toldos apply even to other things. Kesuvos 60a discusses Mefarek regarding suckling from animals.