There is a teaching to the same effect: This only applies when they inherit, but in a case of partnership1 it is prohibited. Then again [the afore-mentioned Rabbis] were sitting together and the question was raised: Can a ger toshab2 annul an idol? Must a worshipper annul it so that a non-worshipper cannot, or perhaps anybody who belongs to them3 can annul it and he belongs to them? — R. Nahman said to them: The more probable view is that a worshipper must annul it and a non-worshipper cannot. Against this is quoted: If an Israelite found an idol in a public place, before it comes into his possession he may ask an idolater to annul it, but after it comes into his possession he may not ask an idolater to annul it because [the Rabbis] declared: An idolater can annul the idol belonging to himself or to another idolater whether he worships or does not worship it.4 What means 'he worships it' and what means 'he does not worship it'? If I say that in either case it refers to an idolater, then it is identical with 'belonging to himself or to another idolater'! Must we not then suppose that the subject of 'worships' is an idolater and of 'does not worship' a ger toshab, and deduce from it that a ger toshab can also annul? — No; I can always tell you that in either case it refers to an idolater, and when it is argued that it is then identical with 'belonging to himself or to another idolater,'[the reply I make is] that in the first clause it means when each of them [worships] Peor or each [worships] Mercurius,5 whereas in the second clause it means when one [worships] Peor and the other [worships] Mercurius.6 Against this is quoted: 'Who is a ger toshab? Any [Gentile] who takes upon himself in the presence of three haberim7 not to worship idols. Such is the statement of R. Meir; but the Sages declare: Any [Gentile] who takes upon himself the seven precepts 8 which the sons of Noah undertook; and still others maintain: These do not come within the category of a ger toshab; but who is a ger toshab? A proselyte who eats of animals not ritually slaughtered, i.e., he took upon himself to observe all the precepts mentioned in the Torah apart from the prohibition of [eating the flesh of] animals not ritually slaughtered. We may leave such a man alone with wine,9 but we may not deposit wine in his charge even in a city where the majority of residents are Israelites.10 We may, however, leave him alone with wine even in a city where the majority of residents are heathens; and his oil is like his wine.' How can it enter your mind to say that his oil is like his wine; can oil become nesek!11 [The wording must be amended to] his wine is like his oil,12 but in every other respect he is like a heathen.13 Rabban Simeon says: His wine is yen nesek. Another version [of Rabban Simeon's statement] is: 'It is allowed to be drunk [by Israelites].' At all events it teaches that 'in every other respect he is like a heathen.' For what practical purpose [is this mentioned]? Is it not that he can annul an idol in the same manner as an idolater?14 — R. Nahman b. Isaac said: No; it is in connection with his power to transfer or renounce ownership;15 as it has been taught: An apostate Israelite who publicly observes the Sabbath16 may renounce his ownership, but if he does not observe the Sabbath publicly he may not renounce his ownership because [the Rabbis] said: An Israelite may transfer or renounce his ownership, whereas with a heathen this can only be done by renting [his property]. In what way? — [One Israelite] can say to [another Israelite], 'My ownership is acquired by you; my ownership is renounced in your favor,' and the latter has thereby acquired [the property]17 without the necessity of a formal assignment.

http://halakhah.com/rst/nezikin/35b%20-%20Avodoh%20Zoroh%20-%2036a-76b.pdf

Says R' Katz, "Following the trend started in the 1960s by the famous archaeologist Vendyl Jones, many non-Jews have become convinced of the truth of the Torah and identify themsleves as Noahides. Or as pointed out in the new book "The World of the Ger" (by R.Chaim Clorfene - author of "The Path of the Righteous Gentile" and "The Messianic Temple", and R.David Katz), written for the growing number who wish to go a stage further and become Gerei Toshavim, the more correct term is 'Noahites'.

The Ger Toshav is basically a spiritually evolved Ben Noach who is unable or unwilling to undergo full conversion, but who nevertheless wishes to reside amongst and formally affiliate himself - to become nilveh - attached to the Jewish People, together with the Yisroel, Kohen and Levi, to become its "Fourth Kahal" (Sifri, Devarim 23:3).

The Chidushei Griz p.82 (R.Y.Z. Soloveitchik) shows that even in the absence of the Yovel, the Rambam, Raavad and all other authorities agree that the status of ger toshav has never gone out of existence, albeit with reduced rights.

The Israeli Chief Rabbinate recently officially recognised a Ger Toshav for the first time in 2500 years, a George Streichman of a Jewish father, for purposes of the Shmitta years, to whom, according to R.Kook, R.Herzog and R.Ovadiya Yosef, it is preferable to sell the Land of Israel to, rather than to an Arab Muslim.
. Interesting sha'alos arise for this contemporary Ger Toshav e.g. can he count for a minyan, can he be called up to the Torah, can his wine be drunk, are we obligated to give him sustenance, how much of the Shabbos can he observe, can he continue to eat non-Kosher, does he require milah, can he perform levayas hameis, be an eid, answer amen, answer a zimun etc etc.

In Chazal there are references to other categories of gerim e.g. ger b'poal, ger b'koach, ger b'emess, ger gamur, ger sha'ar, ger vadai, ger giyura, geriei arayos, gerei chalomos, gerei Mordechai v'Ester, gerei aral v'totav, gerei umos haolam, ger tzedek bdiyeved, ger tzedek l'chatchila, and of course the famous self-made gerim gerurim who will not be able to withstand the test of the Milchemes Gog u'Magog and whose insincerity will at that time be exposed (Avodah Zara 3).

Many Noahites around the world today have studied enough Torah, that if it was more formally available would be keen to upgrade to the status of Ger Toshav and to voluntarily observe more than just the Seven Noahite commandments and to live in Eretz Yisrael, which could have Aliyah implications in the future. Indeed some hold that the Geulah depends on the reinstitutionalisation of the Ger Toshav: "The ger will join them and be attached to the House of Yaakov" (Yeshaya 14).
Included amongst other topics discussed in the book are whether Yisro became a ger toshav or a ger tzedek, the history and status of the Queen of Shva, and on the whereabouts of the Aron Hakodesh.