Gemara

(Mishnah): If a cucumber was planted in an Atzitz (flowerpot; it has no hole), and it grew outside the pot, (that part outside nurtures from the ground. Since entire plant nurtures from it,) the entire plant is Tahor;

R. Shimon is Metaher only the part outside the pot.

Shabbos 95a (Mishnah): If one detaches something that was growing in an Atzitz with a hole, he is liable. If the Atzitz does not have a hole, he is exempt;

R. Shimon exempts in both cases.

(Abaye) Question: In our Mishnah, R. Shimon exempts in both cases. This shows that he equates an Atzitz with a hole to one without a hole;

Contradiction (Beraisa - R. Shimon): The only difference between an Atzitz with a hole and one without a hole is Hechsher of seeds. (If the Atzitz has a hole, it is as if the contents are growing in the ground. They cannot become Huchshar to be Mekabel Tum'ah.)

Answer (Rava): Regarding everything (else) he considers the contents detached. Tum'ah is different, for the Torah was Metaher seeds liberally - "Al Kol Zera Zeru'a Asher Yizare'a."

108a (Abaye): If one uproots mushrooms growing on the handle of a bucket, he is liable for uprooting something from where it grows.

Question (R. Oshaya - Mishnah): If one detaches something that was growing in an Atzitz with a hole, he is liable. If the Atzitz does not have a hole, he is exempt (because its contents do not grow from the ground. The same applies to mushrooms!)

Answer: It is abnormal to grow something in an Atzitz without a hole. It is normal for mushrooms to grow on a bucket.

Menachos 84b - Question: A Beraisa permits bringing Bikurim from what grows on the roof, in an Atzitz... All the more so one may bring from what grows in mountains or canyons!

Answer: The Beraisa permits these for Menachos (but not for Bikurim.)

(Beraisa #1): One may bring Bikurim from the following, and recite (Viduy Bikurim - Devarim 26:3-10): produce that grew on the roof, in an Atzitz (flowerpot), or on a boat.

Contradiction (Beraisa #2): One brings Bikurim from these, but he does not recite.

Answer (for Reish Lakish): One brings and recites for produce that grew on the roof of a cave (this is like regular land), in an Atzitz with a hole, or on a Cheres (earthenware) boat;

One brings and does not recite for produce that grew on the roof of a house, in an Atzitz without a hole, or on a wooden boat.

Berachos 47b (Mishnah): One who ate Tevel (does not join for a Zimun).

This refers even to Tevel mid'Rabanan, e.g. it grew in an Atzitz without a hole.

Rishonim

Rosh (Teshuvah 2:4): Orlah applies to what grows in earth on the roof. In Menachos we say that one brings Bikurim that grew on the roof of a house, but he does not recite. This is because Bikurim must be from the best of your land. However, it is considered attached in every way. We exempt only a portable Atzitz without a hole. It is not planted in the ground, and it is not normal to plant this way.

Rashi (95a DH ha'Tolesh): One who detached from Atzitz Nakuv is liable, for it is like something attached, since it nurtures from the ground. Through the hole, it 'smells' (absorbs) moisture from the ground, even if the hole is in the side.

Rashba (3:341): This is only when the hole is even with the trunk covered in earth of the Atzitz, but not if it is above this. If we would not say so, an Atzitz without a hole would be like an Atzitz Nakuv!

R. Mano'ach (Hilchos Sukah 5:2): The Yerushalmi asked whether one may use gourds in an Atzitz without a hole for Sechach. It did not resolve this. It seems that it is permitted, for one who detaches from an Atzitz without a hole on Shabbos is exempt. However, perhaps we decree not to, lest one use gourds from an Atzitz Nakuv.

Poskim

Shulchan Aruch (OC 336:7): One may not detach from an Atzitz, even without a hole.

Beis Yosef (DH v'Asur): Even though we exempt one who detached from Atzitz without a hole, when the Mishnah says 'exempt', it is forbidden mid'Rabanan.

Taz (7): This implies that one is liable only for an Atzitz with a hole. Even though we obligate one who detaches grass growing on the handle of a Kli (Sa'if 5), the Gemara said that this is because it normally grows there. It is not normal to grow vegetation in an Atzitz without a hole.

Mishbetzos Zahav: In Sa'if 10, we forbid smelling an attached Esrog, lest one detach it. It seems that this is even if it is growing in an Atzitz without a hole. Even though this is like a decree for a decree (even if one detached it, this is only an Isur mid'Rabanan), we forbid because there is a good chance that one would come to transgress.

Shach (9): Some obligate for a wooden Atzitz (without a hole), but exempt for a Cheres Atzitz. Some say oppositely. The Beis Yosef (YD 294 DH u'Mah she'Chasav v'Al) forbids to uproot even from what grows on the roof.

Mishnah Berurah (41): One may not water vegetation in an Atzitz, even if it is in an upper story.

Kaf ha'Chayim (48): The Shulchan Aruch here and in YD does not distinguish between wood and Cheres. If it is considered attached only if it is Nakuv. If not, the Chiyuv for detaching is only mid'Rabanan. This is regarding vegetation. Regarding trees, even if it is not Nakuv, it is considered Nakuv. This is like the Yerushalmi and the Rambam.

Kaf ha'Chayim (51): If something leans outside of the Atzitz over the ground, regarding detaching this is like something attached, even if he detaches from the part inside the Atzitz, since it is attached to what is outside.

Chayei Adam (51:17): If one of the five grains grew in an Atzitz without a hole, and he made bread from it, he does not bless ha'Motzi on it, for this is not called (growing from) the ground (like the Yerushalmi says). Rather, he blesses Borei Minei Mezonos. In any case he blesses Birkas ha'Mazon. (We learn from Berachos. One who ate Tevel does not join for a Zimun. The case is, he ate Tevel from an Atzitz without a hole. Had he tithed it, he would join for a Zimun. I.e., he blesses Birkas ha'Mazon.) Likewise, he does not bless Borei Pri ha'Adamah on what grows from an Atzitz without a hole, for only what is attached to the ground is called Adamah. We would have said that sending away the mother bird does not apply to a nest on a man's head, if not for a verse that calls this Adamah (since man is called Adamah - Chulin 139b and Rashi DH va'Adamah). It is not clear whether one blesses Borei Pri ha'Etz on fruits from an Atzitz without a hole. Perhaps it is not called Pri, or perhaps it is not called Etz.

Chayei Adam (152:3): It is not clear whether a Lulav that grew in an Atzitz without a hole is Kosher for the Mitzvah.

Nishmas Adam (1): Do not say that it is Pasul because it is not called 'Etz'. Orlah applies to such trees! We exempt from Bikurim only because it says "Admasecha". All the more so, if the branches extend outside of the Atzitz (it is called Etz), like the Mishneh l'Melech (Bikurim 2:9) said. All agree that what grows outside is Tahor. Tana'im argue only about what is inside. All the more so what grows on the roof or in houses with a dirt floor (is called Etz), for even Bikurim are brought from it. However, if the house does not have a dirt floor, even what is in an Atzitz Nakuv is not called a tree even regarding Orlah. We obligate a tree growing in an Atzitz only because the roots break through.

Nishmas Adam (DH v'Emnam): In the Yerushalmi, R. Yochanan says that Orlah applies to a tree planted in a house. It is exempt from Ma'aser, for it is not "ha'Yotzei ha'Sadeh." Shemitah is a Safek, for it says "v'Shavsah ha'Aretz", and it says "Sadcha Lo Sizra." I.e. we obligate in Orlah, for it does not say "Sadeh". The verse of Sadcha Lo Sizra should exempt from Shemitah, but another verse says "v'Shavsah ha'Aretz", and 'Eretz' connotes merely that it is attached, even if it is not in the field. The Rambam (Hilchos Ma'aser 1:10) rules like this. Teshuvas ha'Rosh said that what grows on the roof and in the house is surely obligated in Terumah and everything. This is unlike the Yerushalmi. The Yerushalmi asked whether we bless ha'Motzi on what grew in an Atzitz without a hole. It was obvious to the Bavli that one blesses Birkas ha'Mazon. Ha'Motzi is a question, for perhaps this is not called Aretz, since it is not attached. We find that Moshe enacted the first Berachah of Birkas ha'Mazon, even though surely they did not bless ha'Motzi Lechem Min ha'Aretz on manna. The Yerushalmi would also be unsure about Borei Pri ha'Adamah. However, there is no doubt about Borei Pri ha'Etz. The exemption from Orlah is not because it is not called Etz, rather, because it says "u'Nta'atem", and this is not the normal way of planting.

Nishmas Adam (DH v'Hinei): The Yerushalmi asked whether a gourd (in an Atzitz without a hole) is considered detached, to be used for Sechach. It did not ask Stam whether it may be used for Sechach, i.e. is it called Gidulei Karka (something that grew from the ground)? This is like R. Mano'ach said. The question was only whether Chachamim decreed (to consider it to be attached). However, if it is detached, it should be Pasul, for it is not Gidulei Karka! Rather, even if it grew in an Atzitz without a hole, mid'Oraisa it is called Goren v'Yekev (your granary and winepress; we use the waste (chaff and vines sprigs) for Sechach), since the Torah did not say Eretz or Sadeh. Rather, the Torah said only Pri Etz and Kapos Temarim (and Etz Avos), but did not say Etz ha'Aretz, so even what grew in an Atzitz without a hole is Kosher, as long as we know that it was not grafted. Surely, it is called Pri, for Reish Lakish holds that we bring Bikurim from it. Even though the Halachah follows R. Yochanan, who says that we do not bring, there is no source to say that they argue about this (whether it is called Pri). However, the Rambam (Hilchos Terumos 2:1) obligates only Gidulei Karka, similar to Degen (grain) and Tirosh (wine). If so, perhaps we similarly allow for the Arba'ah Minim only (Gidulei Karka,) like Kapos Temarim. This requires investigation.

Keren Orah (Menachos 70a DH v'Aidi): Some Acharonim disqualify Arba'ah Minim that grew in an Atzitz without a hole. I disagree. The Yerushalmi asked about ha'Motzi, since it is not called growing from the ground, but surely one blesses Birkas ha'Mazon mid'Oraisa, for it is bread. We say that it is Kosher for Menachos. The Gemara was unsure about using for Shtei ha'Lechem wheat that fell down in clouds (Menachos 69b). The primary Perush is like Tosfos says, that it was a miracle. Also Borei Pri ha'Adamah is a Safek. Berachos 40b says that we bless sheha'Kol on something that does not grow from the ground. This connotes one blesses Borei Pri ha'Adamah on what grows in an Atzitz without a hole, for it grows from the ground.