What happens to his avadim, who are minors or adults at the time of death: Kiddushin 22b-23a
Acquiring his land by building a fence around it, atop an existing fence: Eruvin 25a
Acquiring his land by improving it: Eruvin 25a
Gezel haGer - Property stolen from a ger, who died without leaving behind family
Goes to a kohen, who owns it entirely: Zevachim 44b
Other Issues
A person who acquires a convert's property should perform a Mitzvah with some of it; he acquired wealth without effort, and so he needs this merit in order for it to remain in his hands. Suggested Mitzvot include acquiring a Torah and writing Tefillin: Eruvin 64a-b