Paine wrote:How does an Ancap-libertarian/Voluntarist determine what can be and what can't be someone's property? How do you determine that Joe has more of a right to the crude oil at site X than Tim? How do you determine that Mr. Monocle has more of a right to the land than his tenant farmers? What gives one person more of a right to land or a natural resource than another? What is the basis of such property? Let's see some of that core philosophy.
This has been done to death in a variety of threads, but for your benefit I'll knock together a few basic elements for you. As Murray Rothbard said: "The libertarian creed rests upon one central axiom: that no man or group of men may aggress against the person or property of anyone else. This may be called the "nonaggression axiom." "Aggression" is defined as the initiation of the use or threat of physical violence against the person or property of anyone else. Aggression is therefore synonymous with invasion."
The nonaggression principle is dependent on property rights, since defining what aggression is depends on what our property rights are. If you hit me, it is aggression because I have a property right in my body. If I take from you the apple you possess, this is trespass — aggression — only because you own the apple. One cannot identify an act of aggression without implicitly assigning a corresponding property right to the victim.
A system of property rights exists to assigns a particular owner to every scarce resource. Without property rights, there is always the possibility of conflict over contestable (scarce) resources and under the NAP this is invalid. As Hans Hermann-Hoppe has shown, the assignment of ownership to a given resource must not be random, arbitrary, particularistic, or biased, if it is actually to be a property norm that can serve the function of conflict-avoidance. Starting with the universal right of self-ownership, this property right claim is valid because the person themselves has the best claim on the property of their person which avoids conflict and permits the peaceful, productive use of the resource in question. It is also universalizable.
In terms of external property, then, as Kinsella said "Unlike human bodies external objects are not parts of one's identity, are not directly controlled by one's will, and — significantly — they are initially unowned. Here, the libertarian realizes that the relevant objective link is appropriation — the transformation or embordering of a previously unowned resource, Lockean homesteading, the first use or possession of the thing. Under this approach, the first (prior) user of a previously unowned thing has a prima facie better claim than a second (later) claimant, solely by virtue of his being earlier." The acquisition of external objects is indeed fundamental to maintain and further one's life. Hence, the right to ownership of external objects is automatically implied by the right of self-ownership and the deprivation of owned property is an act of aggression.
Hence, back to your question. The only assignment of external property titles that is not random, arbitrary, or particularistic and which is assigned based on an objective, ascertainable link between an owner and the resource claimed, is one that is based on Lockean "first-use-first-own" and contractual transfer of title. Latecomers' claims are inferior to those of prior possessors or claimants, who either homesteaded the resource or who can trace their title back to the homesteader or earlier owner.
(Note also, the distinction between ownership and possession. The first is the right to control, use or possess a resource while the latter is just the physical control of the resource.)
On a final note, non-scarce things where my subsequent possession of something that you own does not infringe on your rights or alter your continued ability to own the thing does not constitute aggression. This is why intellectual property is not regarded as "true" property by libertarians.