The statist implementation of private property presently depends on central control of cadastral maps and land registers, operating under state monopolies.
Clearly this wouldn't be an option in a stateless society, which isn't a problem for classical anarchism (communism, collectivism, mutualism, or individualism) since its goal is to abolish private property anyway.
In the absence of state enforced property rights, ownership defaults to mutual respect predicated on a natural desire for security and social harmony. This is termed "occupancy and use" (also referred to as "possession property"), wherein the owner is whomever is commonly recognised* to occupy, possess, or use the asset in question. Disputes may either be settled by mutual aid, negotiation, arbitration, adjudication, or if all else fails by force.
[*NOTE "commonly recognised" infers that property is not automatically deemed to be abandoned the instant an owner ceases to actively occupy or use it.]
In classical anarchism the onus is on establishing ownership by peaceful means. Attempting to occupy land or seize assets, which are commonly recognised to be occupied or used, would thereby constitute aggression, placing the perpetrator in conflict with other anarchists.
The political theory of minarchism gets around this issue by retaining a minimal state and its related security force (along with the resultant taxation), mainly for the purpose of upholding private property rights.
Anarcho-capitalism is an ideology that seeks to marry a stateless society with those same private property rights. It therefore faces a significant challenge in upholding private property rights in the absence of a state, without imposing its rules by force.
This isn't an issue for any property with an incumbent occupier or user: including but not limited to a tenant, renter, leaseholder, or guards... not withstanding the economic viability of such arrangements. Problems only arise where an absentee owner has left the property vacant or unused, and therefore dependent on mutual respect.
Where the owner is an absentee landlord, it may well be that neighbouring occupiers are not cognisant of the status of the property, unaware of the owner's identity, unwilling to get involved, or simply aren't prepared to lend mutual aid to someone they have no meaningful social interaction with.
The presence of buildings, fences, private property notices, and for rent signs are not reliable indicators of abandonment, and may go missing, collapse, or degrade due to erosion, natural ingress, or vandalism. For ownership of a vacant property to stand any chance of being respected, said property must be well maintained, thereby incurring costs. However in the absence of any resistance it remains possible for a third party to non-violently establish occupancy & use of said vacant property... leaving the erstwhile owner with the option of initiating force in order to reclaim it... which would disrupt social harmony putting them at odds with other anarchists.
Therefore for ancaps to successfully implement private property rights within a stateless society, they must either:
A. Convince everyone else to adhere to their rules. This seems somewhat unrealistic.
B. Convince everyone else to enshrine absentee ownership as a universal human right. This also seems somewhat unrealistic.
C. Somehow agree to establish a universal register of property owners (either a by way of a centralised repository or via a distributed network). This seems somewhat unrealistic given other anarchists aim to abolish private property... and even ancaps might struggle to agree how such an authority would be organised, controlled or funded given their ostensible opposition to tax and statism.
D. Establish a working network of privately regulated private registers who agree to share data. Again this seems somewhat unrealistic since other anarchists would simply refuse to recognise any such authority.
E. Resort to force to impose A, B, C, or D... thus rendering anarcho-capitalism inherently authoritarian and not anarchist.
Hence since anarcho-capitalism almost certainly depends on force, it is therefore inherently authoritarian, and is not anarchism... unless anyone has any other suggestions???
Of course the obvious solution would be for ancaps to ditch private property rights for occupancy and use, which by their own account would appear to meet most of their objectives, thereby rendering anarcho-capitalism indistinguishable from individualist anarchism. The bottom line is that if an absentee landlord is unable to maintain their own property rights, then tough shit they aren't entitled to it.