Although I consider myself to be firmly anarcho-capitalist, I disagree with ~90% of the anarcho-capitalists I've met regarding property rights (in particular, on land claims).
The position I typically hear is that property rights are determined by the transformative work someone puts into an unowned piece of material, and the property rights act as an absolute defining line for who has control over it. I think this view is misguided, and is incubated by living with a state enforcer of property rights for many decades. Effectively, a monopolistic police force allows for end-all-be-all consensuses on property claims to be made, which is not how a set of competing DRO's would act.
Instead, I believe that property rights in Ancapistan will work much the same way as prices. I.e. they are ultimately subjective, and while people can easily come to an agreement about what is a ridiculous price, they can not easily come to a consensus on what is an optimal price. This is a _feature_, and not a bug of free market economics, because it allows for human desire to self-regulate human desire.
The issue with imagining an individual's property claim as objective is analogous to imagining the price a merchant sets for a good as objective. While you can objectively survey what people think a particular price should be and survey who they think should own an object, that does not make the claim itself any less subjective. (In fact, that would be the reason one falls-back to a survey in the first place.)
For example, what exactly defines "transformative work"? What if others consider themselves to have put more work in the material than you? What if others consider the work you put into the material to have made it worse? How is the conversion ratio between different kinds of work calculated?
No matter what rationalizations are used or how many steps towards property rights are inserted, subjectivity is still there. And that should be expected, because property rights themselves exist _exclusively_ within the minds of conscious beings, not as an exact physical phenomenon. Do not think I'm implying this means property rights are useless, because that would be as ridiculous as claiming food prices serve no useful purpose.
So if property rights are subjective, then how can anybody be certain that they "own" an object enough to use it? In my view, the first line of defense is common sense, but that's true with or without anarcho-capitalism. However, for more complex and higher-stakes claims, I believe there would be companies computing some sort of "ownership index" over the property, similar to how stocks are priced. This conceivably could be DRO's themselves, or a pool of arbitrators trying to efficiently come to a consensus when conflicts arise.