Gemara

16b (Beraisa - R. Yosi b'Rebbi Yehudah): Ropes [surrounding an area in a valley] permit only up to Beis Sa'atayim for one or two people, but three get up to [Sa'atayim for each, in all] six Beis Sa'im;

Chachamim say, even an individual gets as much as he needs, just there may not be Beis Sa'atayim free [more than is needed].

18a (Mishnah - R. Yehudah): Pasei Bira'os [around a well] may surround up to Beis Sa'atayim.

Chachamim: Sa'atayim is the limit for a garden or Karfef (an enclosed area without a roof). There is no limit for a Dir (a field where one grazes animals to fertilize it), Rechavah (a Chatzer in back of houses) or Chatzer.

23a (Mishnah): R. Yehudah ben Bava taught that one may carry in a garden Sa'atayim, as long as there is Shomirah (a watchman's shack) or Beis Dirah (house for residence) inside, or it is close to the city.

R. Yehudah says, even if there is only a pit or cave inside, one may carry inside;

R. Akiva says, even if none of these is inside one may carry inside, but only if it is Sa'atayim.

R. Eliezer says, if the length exceeds the width, even by one Amah, one may not carry inside.

23b (Rav Bivi): The Halachah follows R. Akiva.

(Mishnah - R. Shimon): Roofs, Chatzeros and Karfifos are considered like one Reshus for Kelim that were Shoves (began Shabbos) in them, but not for Kelim that were Shoves in the house.

(Beraisa): If a Karfef more than Beis Sa'atayim was Hukaf l'Dirah (surrounded for needs of dwelling):

If the majority was seeded [it is not proper for Dirah], it is like a garden, so one may not carry in it on Shabbos;

If the majority was planted [with trees], it is like a Chatzer, so one may carry in it.

(Rav Huna brei d'Rav Yehoshua): The Reisha forbids only if the seeded area is more than Beis Sa'atayim. If not, one may carry in it;

24a - Inference: If the minority was seeded, it is permitted.

Version #1 (Rav Huna): This is only if [the seeded area] is less than Beis Sa'atayim. If it is Beis Sa'atayim, it is forbidden.

This is like Chachamim [of R. Shimon. They forbid transferring between a Karfef and a Chatzer, so these places forbid each other.]

Version #2 - R. Yirmeyah mi'Difti - (Rav Huna): This is only if [the seeded area] is at most Beis Sa'atayim. If it is more, it is forbidden.

This is like R. Shimon. (Chachamim forbid even Beis Sa'atayim.)

(Rav Nachman): If one made an opening [from his house] to a Rechavah, he may carry in all of it.

This is only if he opened and later surrounded it, but not if he surrounded and later opened.

67b (R. Yochanan): If a Karfef more than Beis Sa'atayim was not Hukaf l'Dirah, even if it is one or two Beis Kor (30 Sa'im), one who throws into it [from Reshus ha'Rabim] is liable.

This is because it has a proper wall. It is merely lacking dwellers.

Rishonim

Rambam (Hilchos Shabbos 16:1): If a place was not Hukaf l'Dirah, rather, it is used for the airspace, e.g. a garden, orchard, or one who surrounds a place to guard it, if the walls are at least 10 Tefachim tall, it is Reshus ha'Yachid to obligate one who throws or passes to there from Reshus ha'Rabim. One may carry there more than four Amos only if it is Beis Sa'atayim or smaller.

Rosh (2:2): If a Karfef less than Sa'atayim was not Hukaf l'Dirah, it is not clear whether it is like Sa'atayim, and Rabanan [of R. Shimon] forbid carrying from it to the Chatzer, and R. Shimon [whom we hold like] forbids carrying from it to the house. He holds that roofs, Chatzeros and Karfifos are like one Reshus only for Kelim that were Shoves in them, but not for Kelim that were Shoves in the house. It seems that less than Sa'atayim is like Sa'atayim. If not, we must say that R. Shimon and Rabanan argue about exactly Sa'atayim. If it is more than Sa'atayim, all forbid carrying even inside more than four Amos, and if it is less, one may carry even into the house. However, perhaps they argue about Sa'atayim, and about slightly less, until it is a full Amah less, just like R. Eliezer forbids only if the length exceeds the width by a full Amah. We distinguished between less than Sa'atayim and Sa'atayim when the minority was seeded. This is not a proof. Since the minority was seeded, if it is less than Sa'atayim it is not important, and it is Batel. When the majority was seeded, perhaps even less than Sa'atayim forbids. It seems that less than Sa'atayim is like Sa'atayim. The Mishnah [of R. Shimon] taught Karfef Stam, which connotes any Karfef not Hukaf l'Dirah. Since one may carry in it, it must be at most Sa'atayim. He and Rabanan have the same argument when it is less.

R. Yehonason (7a): If the Mechitzos stood by themselves, e.g. mountains or clefts in a rock, or he did not intend to dwell there, even if afterwards he built a Dirah there, this is not Hukaf l'Dirah.

Tur (OC 358): Sa'atayim is permitted without Shomerim or a Beis Dirah, just like Chatzer ha'Mishkan was permitted without any Dirah, just it was surrounded by curtains.

Ritva (16b DH v'Chachamim and DH v'Chol): Chachamim permit an individual as much as he needs, even if it is more than Sa'atayim. Since it was made for this, it is better than a Karfef not Hukaf l'Dirah. This is only in the Midbar. In a settled area, an individual gets only up to Sa'atayim. R. Yosi b'Rebbi Yehudah permits a Rabim (at least three) six Sa'im, and Rabanan and R. Yehudah permit as much as they need.

Poskim

Shulchan Aruch (OC 358:1): Any enclosure not for the sake of Dirah, e.g. a garden, orchard or shack merely for Shemirah, Chachamim forbade carrying more than four Amos in it if it is more than Sa'atayim.

Taz (1): More than Sa'atayim is called Karmelis. Sa'atayim is called a Karfef. It is one Reshus with a Chatzer for Kelim that were Shoves in them, but not for Kelim that were Shoves in the house.

Kaf ha'Chayim (10): One may not carry from the Karfef to a Karmelis.

Mishnah Berurah (1): "Dirah" is residence of man and what he uses.

Mishnah Berurah (4): Even though the shack is for the Shomer to live in, he does not dwell there for its own sake, rather, to guard the space in front of it. This is not an important Dirah. It is like a surrounded garden or orchard. Even if it has a roof, it is not important Dirah. See what I wrote in Bi'ur Halachah 362:1.

Bi'ur Halachah (362:1 DH Oh): If a storehouse is more than Sa'atayim, it is like a Karfef, for it is merely for Shemirah, and not for Dirah. It is like a Rechavah. However, perhaps it is better, for it has a roof. Rashi (22b DH Kol) says that a roof does not help if it is not for Dirah. Rashi learned from "any Dirah for the use of airspace." The Rambam explains unlike Rashi. He could hold that a roof helps! Perhaps Rashi agrees that an important building like a roofed storehouse is not called a Karfef at all. The Pri Megadim (358) was unsure whether a roof helps. If the storehouse serves also other needs of man, surely it is Dirah.

Kaf ha'Chayim (6): If a Karfef has a roof, one may carry in it.

Mishnah Berurah (5): Even though mid'Oraisa, anything surrounded by walls 10 Tefachim tall is Reshus ha'Yachid and one may carry in all of it, Chachamim forbade if it is more than Sa'atayim and not Hukaf l'Dirah. This is because it looks a little like Reshus ha'Rabim or Karmelis. Therefore, one may not carry in it more than four Amos, like in Reshus ha'Rabim or Karmelis.

Kaf ha'Chayim (8): A Karfef above Sa'atayim is forbidden even if one person owns it, and all the more so if two own it. An Eruv does not help.

Shulchan Aruch (ibid.): If it is Sa'atayim, one may carry in all of it. If it was Hukaf l'Dirah, even if it is several Mil, one may carry in all of it.

Beis Yosef (DH u'Mah she'Chasav Chachamim): The Halachah follows R. Akiva, who does not require that it be Hukaf l'Dirah [if it is no more than Sa'atayim].

Kaf ha'Chayim (9): Shulchan Shel Arba rules like the Ritva, who permits three people as much as they need, but some disagree.

Rema: See the law of Stam cities in 401:1.

Mishnah Berurah (13): There we say that Stam we say that it was Hukaf l'Dirah, for it is normal to surround only after building houses first.

Rema: Some say that our Stam Karfifos are Hukaf l'Dirah. It is normal to first make an opening, and later surround.

Mishnah Berurah (14): This is when the house is open to them.

Mishnah Berurah (15): The Rema means that when we do not know, we assume that the Karfef was built after the houses for the use of the house, for this is the norm. If this is not the norm, it is forbidden.