I agree with David Musick that it is worth examining the concept of property rights. I would not approach this with the idea of stripping anyone of their property (so jerk those knees back down). Rather, consider a voluntary society (a space station, say), and consider in what ways property rights are useful and beneficial, and in what ways other ways of organizing resources may work better.
This is a utilitarian rather than natural-rights approach to property rights (and other social institutions) and is IMO well within the mainstream of extropian thought.
We are already aware of situations where other methods than property rights are used to control access to resources. Within families there are many resources which are commonly available to all. Within firms it is also common to organize the companies efforts on a command basis rather than by means of a market. Even in society as a whole, many resources which difficult to manage with market mechanisms (like unpolluted air, and whales) are handled in other ways.
There is a "theory of the firm" in economics which explores in detail the question of when markets vs other organizational structures should be used within corporations. This is not an immoral enterprise, but it gives us useful information on the nature of reality which we can use to guide our efforts.
I also agree with David that property rights are a social construct and in that sense can be considered "fictional" (perhaps "cultural" would be a better word). We had a discussion a few months ago about abstract property rights, like intellectual property, ownership of the EM spectrum, solar energy rights, unobstructed views, whaling rights, and other entities which some people have tried to allocate with market mechanisms. For some people it was obvious which things are "natural" property and which are not, but in my view it comes down to social agreements about what will be treated as ownable.