Gemara

118b (Beraisa - R. Meir): If Levi owned a tree in Yehudah's land, what grows out of the stump or roots belongs to Yehudah;

R. Yehudah says, what grows out of the stump belongs to Levi. What grows out of the roots belongs to Yehudah.

(Mishnah - R. Meir): Orlah applies to what grows out of a stump or roots (whatever grows in the first three years is forbidden);

R. Yehudah says, Orlah applies to what grows out of the roots, but not to what grows out of the stump.

Had they argued only about a tree in another's field, one might have thought that R. Yehudah argues only about money, but regarding Orlah, an Isur, he admits (that Orlah applies even to what grows from the stump). Had they argued only about Orlah, one might have thought that R. Meir argues only about an Isur, but regarding money he admits.

Bava Basra 81a (Mishnah): If Reuven bought two trees in Shimon's property, he did not acquire land (with them);

R. Meir says, he acquired land.

Reuven owns whatever grows from the stump. Shimon owns whatever grows from the roots.

82a (R. Yochanan): Whatever is above the ground is considered the stump. Whatever is below the ground is considered the roots.

Gitin 22a (Abaye): If the hole of a flowerpot is in Eretz Yisrael, and the foliage is in Chutz la'Aretz, we follow the hole (for Terumah, Ma'aser...)

(Rava): We follow the foliage. (It is as if it it grows in Chutz la'Aretz.)

They argue only if the plant did not take root in the ground.

Question: Perhaps even if it took root, they argue like the following. Tana'im about whether we follow the roots or the foliage!

(Mishnah - R. Meir): If Kelim owns a hill, and Shimon owns at the bottom, what grows on the incline (the side of the hill) belong to Levi;

R. Yehudah says, they belong to Shimon.

Answer: The Mishnah explains that they argue about something else. R. Meir says that Levi could remove his soil, so all that grows is due to him. R. Yehudah disagrees, for Shimon could fill his airspace with soil.

Rishonim

Rambam (Hilchos Ma'aser Sheni 10:19): A tree that grows out of a stump is exempt from Orlah. Orlah applies to what grows out of the roots.

Question (Ri Korkus, Kesef Mishneh, Kaftor va'Ferach 54): This is unlike the first Tana in the Tosefta (Orlah 1:4), who obligates what grows out of a stump or roots, and unlike R. Yehudah, who obligates only what grows out of a stump!

Answer #1 (Ri Korkus): The Rambam learns from Bava Basra that what grows out of a stump is like the tree itself, so it belongs to the buyer. What grows out of roots is like a separate tree growing from the seller's ground. The Rashbam explains like this.

Answer #2 (Kesef Mishneh): The Rambam had a different text in which the first Tana obligates only what comes from the roots.

Rebuttal (Machaneh Efrayim and Rashash, in Likutim in Frankel Rambam): Clearly, the Rambam rules like R. Yehudah in Bava Metzia. We cannot attribute this opinion to the first Tana!

Noda b'Yehudah (2 YD 185): In the Tosefta, R. Yehudah obligates what grows out of a stump. R. Yeshayah Fik switched the text so that he obligates what grows from the roots (like Bava Metzia 119a), for this is more reasonable, and challenged the Kesef Mishneh. I say that the Kesef Mishneh held that the Rambam rules like his text of the first Tana. We do not rule like R. Yehudah against R. Meir when R. Meir's opinion is taught Stam. In Bava Metzia R. Meir's opinion is taught in his name, but perhaps it is a different Beraisa. Do not say that the Gemara did not bring the Tosefta for it is unreliable. Rather, it brought the Beraisa to show that R. Meir and R. Yehudah argue in two places.

Rebuttal (Chazon Ish Orlah 2:8): The Gemara says that R. Meir and R. Yehudah argue about this, so it is as if it explicitly ruled like R. Yehudah, based on Eruvin (46b). Also, we do not have a precise Tosefta. We rely on the Gemara against the Tosefta. The Yerushalmi supports it.

Tosfos (Gitin 22a uved'Ashrush): Abaye and Rava argue about whether the roots or foliage are primary. The Gemara should have said that they argue like R. Meir and R. Yehudah regarding Orlah!

Or Zaru'a (1:326): The Tosefta exempts what grows out of a stump or roots, i.e. of a mature tree. Orlah applies to them if the tree is within three years.

Ra'avad (in Shitah Mekubetzes 118b DH Omar): Really, R. Meir and R. Yehudah argue about whether Peros grow due to the roots or due to the air. Therefore, they argue about whether or not we attribute the Peros to the roots. Surely what grows from the roots is exempt from Orlah, for the years of Orlah already passed! R. Yehudah considers what grows from them to be like a new tree. In the Mishnah, R. Meir and R. Yehudah address each other according to the other's reasoning (granted, you argue about what makes Peros grow, but admit to me that nothing would grow without the soil/airspace).

Ramban (118b DH Ha): All agree that nurturing depends on the roots. Rashi's text says that R. Meir obligates what comes out of a stump or roots. This is wrong, for the Gemara said 'one might have thought that R. Meir admits about Orlah, an Isur (and is stringent).' This shows that R. Meir is lenient.

Acharonim

Lechem Mishneh (Hilchos Shechenim 4:9): Regarding ownership of vegetation between two fields, the Rambam rules like R. Meir and R. Shimon, who attributed the Peros to the Ikar. How can he rule like R. Yehudah regarding Orlah, who exempts what grows from the stump? If Orlah (Isur) is different, we are more stringent to consider new growth like a new tree! The only difference the Gemara found was between money and Isur! We must say that the Rambam saw that the Gemara rules like R. Shimon regarding neighbors, but not for R. Meir's reason. He does not attribute Peros to the Ikar. Rather, it depends on who has more ability to prevent the Peros from growing.

Kehilas Yakov (27 (in old editions, 2:22)): Omer ha'Shichechah asked why the Rosh, Tur and Shulchan Aruch omitted this. The Or Zaru'a rules like the first Tana according to the text of the Ra'avad and Ramban; he must hold like the Noda b'Yehudah. However, regarding money, a Stam Mishnah attributes whatever grows from the stump to the tree's owner, and whatever grows from the roots to the owner of the ground. The Or Zaru'a rules like this. The Gemara said that perhaps we are more stringent about Isur to consider new growth as if it were a new tree, even though for money it is not. All the more so, we must be stringent to say that Orlah applies to what grows from the roots, which even for money is like a new tree! This requires investigation.

Question (Kehilas Yakov 27:2): We count the years of Orlah from when the seed was planted. Even if what grows from the roots looks like a new tree, we should count from when the tree was planted! We must say what grows from a seed is different. It started to sprout from when it took root. However, the Yerushalmi says 'an exempt root exempts', e.g. if a tree was uprooted and even a thin root remained, or a tree is partially in Chutz la'Aretz. The Chazon Ish (2:8) said that the Yerushalmi exempts only a tree that nurtures from the exempt root and other roots. We do not partially obligate what grows. What sprouted from the root is totally liable, like a new tree. This is like Rashi, who says that what grows from the roots is like a new tree. The Ra'avad and Ramban say that R. Yehudah holds that it grows from the air. Since it nutures also from the roots, the Yerushalmi's exemption should apply!

Answer (Kehilas Yakov): The fact that what grows from the roots is liable proves that nurturing from an old root does not exempt a tree less than three years old. Rather, all exempt what grows from the stump (according to the Ra'avad's text) for it is Tafel (secondary) to the stump. If not, Orlah would apply to new branches of old trees! The Ra'avad and Ramban explain why R. Yehudah holds that what grows from the roots is not considered secondary to the root.

Ya'aros Devash (2 Derush 16 DH Emnam): R. Yehudah holds that most growth is from the air, but he admits that some is due to the roots. Regarding Orlah we follow the majority. We do not follow the majority regarding Ma'aser, for it is Yesh Lo Matirim, and not regarding money.

Chazon Ish (Orlah 1:19 DH v'Ha): Toras Kohanim exempts what grows by itself, i.e. what grows out of a stump. A Stam Beraisa in Toras Kohanim is R. Yehudah. Orlah applies to what grows from a seed that fell. The Yerushalmi says that Orlah applies to a tree totally cut, but if something remained, what grows from it is exempt. This Toras Kohanim (brought in Perush ha'Mishnayos Orlah 1:5 DH Sipuk) is taught amidst laws of grafting and Havrachah (inserting vine ends into the ground to grow out). However, Perush ha'Mishnayos (1:2 DH veha'Oleh) says that 'grows by itself' is what man did not plant.