Gemara

(R. Oshaya Ze'ira of Chavriya - Beraisa): There are five things that must be at least one Tefach -- a Shilya, a Shofar, the spine (of a Lulav), a wall of a Sukah, and Ezov (hyssop, for Parah Adumah or Metzora).

(Beraisa - R. Shimon ben Gamliel): A Shofar must be long enough that it is visible from both ends when one wraps his fingers around it.

(R. Parnach citing R. Yochanan): The spine of a Lulav must be a Tefach longer than the Hadas (myrtle).

Sukah 32b (Rav Yehudah citing Shmuel): The Shi'ur for Hadasim and Aravos is three Tefachim. The Shi'ur of a Lulav is four, so it will be a Tefach above the Hadas.

(R. Parnach): The spine of a Lulav must be a Tefach above the Hadas.

Question (Mishnah): If a Lulav has three Tefachim, in order to shake it, it is Kosher.

Answer: It means that if it has three Tefachim and enough to shake it, it is Kosher.

Each of Rav Yehudah and R. Parnach explains according to his opinion (whether the Lulav or its spine must be a Tefach above the Hadas in order to shake it).

Menachos 41b (Beraisa - elders of Beis Hillel and Beis Shamai): There is no Shi'ur of a Lulav.

Question (Mishnah): If a Lulav has three Tefachim, in order to shake it, it is Kosher.

Answer: There is no maximum length of a Lulav, but there is a minimum.

Rishonim

Rambam (Hilchos Lulav 7:8): The Lulav must be at least four Tefachim. If it was any amount (more), it is Kosher. We measure only on the spine, but not from the end of the leaves. The Hadasim and Aravos must be at least three Tefachim. If they were any amount (more), they are Kesherim. If one tied the Lulav (to the Hadasim and Aravos), its spine must extend at a Tefach or more above the Hadasim and Aravos.

Ran (Sukah 15a DH Amar): The Halachah follows R. Yochanan, and not Shmuel, who holds that it suffices for the leaves to extend a Tefach above the Hadas. Presumably, even if the Hadasim and Aravos are extra long, the spine of the Lulav must be a Tefach above them. This is why R. Yochanan and Shmuel said 'a Tefach above the Hadas), and did not simply say four Tefachim with/without the leaves.

Rosh (Rosh Hashanah 3:6): R. Shimon ben Gamliel taught that a Shofar must be long enough that it is visible from both ends when one wraps his fingers around it. It says in Nidah that this is a Tefach. R. Shimon ben Gamliel expressed the Shi'ur this way to teach the reason for the Shi'ur, lest people say that he blows into his hand.

Ran (Rosh Hashanah 7a DH Kedei): He did not explicitly say that the Shi'ur is a Tefach, for he wanted to teach the reason for the Shi'ur. A Tefach is four thumbs. When one holds the Shofar in the other four fingers, and a little sticks out on each end, this equals a Tefach.

Poskim

Shulchan Aruch (OC 586:9): The Shi'ur for Teki'ah is four thumbs.

Question (Beis Yosef DH u'Mah she'Chasav v'Ha and Bach (DH u'Mah (2)): The Ran and Tur say that 'in order to hold it' does not refer to the one who blows it (i.e. it must be as big as his hand). If so, it should have been taught b'Hedya (explicitly) that it is according to the size of the person! Rather, it is the Shi'ur for an average person to hold it, i.e. a Tefach.

Beis Yosef: The Tur is difficult. It was not taught explicitly, but the Shi'ur is in order that it will be visible. This shows that it depends on the one who blows! Rather, the text should say 'it should have been taught Bahadei (with the matters) that are according to the size of the person (Kelim 17:12). The Ritz Gei'us says that he said 'some must stick out on each side' to teach that the Tefach must be Sochek (slightly bigger, i.e. with small spaces between the fingers). The Tur taught that this Shi'ur (in order to see it) is exactly a Tefach, so there is no need to say like the Ritz Gei'us.

Bach (DH u'Mah (2)): I answer that only regarding Shofar, one could have erred to be lenient, that we discuss a Stam person who holds it, i.e. an average Tefach. This is why it was taught with other such matters in Nidah. Therefore (if it depended on the one who blows), it should have been taught with the matters that are according to the size of the person. The fist of Ben Avti'ach was much bigger. When he blows, the Shofar does not show, for it is only an average Tefach. For the Tefach of a Lulav, a small Tefach suffices. There was no need to explain this. Firstly, even if one would err, there is no problem. He will be stringent!

Note: The stringency can lead to a leniency. If he cannot find a Shofar of the bigger size, he will not do the Mitzvah at all!

Bach (ibid.): Also, there is a small difference between the Shi'urim, i.e. two thirds of a thumb-width. People are not normally so particular about this. (Normally, they do not take something so close to the minimum Shi'ur.) Also, presumably the Tefach that must extend past the Hadasim and Aravos is like the Tefach of the Hadas, i.e. a small Tefach, so people will not err. Regarding Shofar, people would come to be lenient. Also, there is a big difference between hands, e.g. of Ben Avti'ach. There is no reason why people would not err. In fact, there is a (misleading) "proof", since it was taught with other Tefachim! Therefore, if it depended on the person, it should have been taught with the others. Since it was not, this shows that it is an average Tefach.

Magen Avraham (18): Four thumbs is for an average person. This is where the thumb is wide.

Mishnah Berurah (54): Four thumbs is a Tefach.

Bi'ur Halachah (DH Dalet): Also R. Chananel says like the Ritz Gei'us. Everything R. Chananel says is a tradition. It seems that this was his text in the Gemara. Also Kol Bo, which is a collection of Teshuvos, connotes like this. Also R. Mano'ach on the Rambam says that all the five Tefachim taught are Sochek. The Rosh holds that the Shi'ur is only mid'Rabanan, lest people say that he blows into his hand. However, Tosfos (Sukah 7b DH Sikech) holds that it is mid'Oraisa, for in Nidah we taught only Shi'urim mid'Oraisa. Also Rashi connotes like this. Even the Rosh agrees that mid'Oraisa there is a Shi'ur in order to blow. This is why we disqualify a Shofar of an Ir ha'Nidachas, because (it is considered to be burned, so) it is less than a Shi'ur. Toras Kohanim connotes like this. All agree that the Shi'ur is so that it is visible on both sides when one holds it. The Ran and Tur say that this is based on an average person. A big person may take a Shofar of an average Tefach, even though when he holds it, it is not visible on both sides. The Ritva disagrees. The Tana in Nidah discusses an average person. A bigger person needs a bigger Shofar.

Kaf ha'Chayim (89): The Levush says that mid'Oraisa, there is no Shi'ur. The Torah discusses a Shofar of any size.

Kaf ha'Chayim (92): Mateh Yehudah says that if the Shofar is less than a Tefach, he was not Yotzei, even if the Shi'ur is mid'Rabanan. However, the Eshel Avraham says that since the Shi'ur is mid'Rabanan, if there is no Shofar around that is a Tefach, Chachamim did not enforce their decree to annul the Mitzvah. (One may blow a smaller Shofar). He connotes that one may bless. Acharonim argue about this. Whenever there is an argument, if no other Shofar is available, one blows it without a Berachah. If later he gets a Shofar that is Vadai Kosher, he blows again without a Berachah.

Shulchan Aruch (650:1): The Hadasim and Aravos must be at least three Tefachim. The spine of the Lulav must be at least four Tefachim, so the spine will extend a Tefach above the Hadasim and Aravos.

Beis Yosef (DH u'Mah she'Chasav Rabeinu): It is known that the Halachah follows R. Yochanan against Shmuel. The Poskim rule like this.

Bach (2): Also, the Beraisa in Nidah supports R. Yochanan.

Mishnah Berurah (1): (Even) if the leaves of the Hadasim and Aravos go above the wood, the wood itself must be three Tefachim.

Mishnah Berurah (2): There is no Shi'ur for the leaves of the Lulav.

Bechori Yakov (1): It is improper to take a Lulav covered with bark. A Tefach of the Lulav must be untied so the leaves can rustle. The leaves do not rustle in a closed Lulav!

Shulchan Aruch (2): There is no upper Shi'ur. Some say that even if he made the Hadasim and Aravos longer, the spine of the Lulav must be a Tefach above them.

Kaf ha'Chayim (9, citing Mateh Yehudah): The Shulchan Aruch connotes that if it is not a Tefach above the Hadasim and Aravos, he was not Yotzei. However, it seems that even this opinion disqualifies only if both other species were at least as tall as the Lulav. However, the primary opinion allows the other species to be taller than the Lulav.

Kaf ha'Chayim (9): Aruch ha'Shulchan disagrees with this. The Shulchan Aruch did not bring anyone who argues with the Ran. Kol Bo brings like the Ran from Ritz Gei'us. The Ritva agrees, and it seems that the Rambam and Mordechai agree. Orchos Chayim brought a dissenting opinion, but most hold that it is Me'akev even if only one species is taller than the Lulav.