This thread raises some interesting issues regarding the whole concept of property; and by this I mean spatially defined property, like land, rights-of-transit or exploitation to the ocean sea floor, airspace, or worlds or even volumes of sidereal space. Personal belongings are a whole other issue.

In our legal system, which is purely arbitrary and based solely on precedent and custom, all property is acquired by sale or trade negotiated with the owner. In fact, the right to sell property is almost the definition of ownership of property. But who determines the first owner? Property is originally acquired by either the violent appropriation of someone else's property, or by grant from some authority which has given itself the charter to dispense and distribute it. It makes me think of the old cartoon which shows two cavemen huddling by a campfire and one tells the other "I've got an idea, let's divide the whole world into little pieces and sell them to people."

There are alternative definitions of property. In ancient Britain, tribes claimed land because the bones of their ancestors were buried there. Some American Indian tribes had no concept of property, although they
claimed exclusive use to the resources on it (the land belongs to everyone, that fruit tree is mine). One possible definition is that the property owner is the one who has developed or occupied it or otherwise controls it, but how does that determine the boundaries and extent of that property which may extend considerably beyond the area that is actually settled? All of these definitions can be trumped by violence. Claims or grants on property presuppose some governmental authority has given itself the right to dispense those claims. This holds little weight when that authority no longer can mobilize the force to enforce those statutes (Spanish Crown land grants in California and Texas): even if an occupying government appears to honor the rituals of private ownership, it often rigs the law so the original owners have little choice but to sell at a loss to the invaders.

Although nominally under the cloak of legality and procedure, land ownership is originated and often perpetuated through either discovery or outright theft and violence, and it remains a civil and negotiated transaction only as long as some judicial (i.e., military) entity can enforce it. At least, that's how humans have always done it. I suspect space real estate law will be just an extension of our past history: send lawyers, guns and money.

Unless humanity voluntarily enters into some kind of treaty structure to define extraterrestrial property and sets up a mechanism to enforce it,
there will be a violent struggle for off-planet resources once their value becomes attractive enough to someone with the means to steal it. And whatever legal structure evolves, it will always be vulnerable to those who think they have the power to get around it.

And of course, if extra-terrestrial civilizations are involved, I'm sure they will have their own definitions of law, capitalism, and property. I'm looking forward to that court case.