Amidst Anarchocapitalist authors such as Murray Rothbard, are there any who discuss the possibility of privately-owned countries?
Private countries would be shares of land owned by investors which would possess their own laws, courts, police and otherwise public services. Such enterprise's profit would come from rent.
I think I could recommend a few writings, although the list is by no means extensive.
If you're interested in works by Anarcho-Capitalists in particular, one individual of interest is Hans-Hermann Hoppe. He is known for advocating for Monarchy as a more 'capitalist' form of government than Democracy. He also wrote on a variety of topics that would be of interest in relation to your question - Anarcho-Capitalist solutions to national defense, gated communities as a form of organization in an Anarcho-Capitalist society, etc.
If I remember correctly, he touches on these topics in the following works:
Furthermore, Neoreactionary thought is largely based in the concept of privately owned countries or "sovereign corporations". These ideas were pioneered by the blogger Curtis Yarvin, under the pseudonym "Mencius Moldbug". A full collection of his works can be found here. Of particular interest in this case are the following posts:
Finally, you might be interested in publications by groups such as the Seasteading Institute, which seeks to, among other things, address the practical and legal issues associated with running a settlement that is located outside the territory claimed by any government.
