Its not your "home" if the countries laws say it isn't. Humans rights say people should not be stateless, however it doesn't mean you auto gain citizenship of the a random country you are born in, same as some don't get your citizenship of your parents origin. You get one or the other as your citizenship, or apply for it.
As a hyperbolic example: Imagine your get a lottery win, buy yourself and your spouse one of those islands and start your own country, suddenly everyone hears about it and lands boats to have babies there, now they are your citizens and you owe the social services to a 1000 babies as is their right as a human.
The first one of course that's what I meant its determined by the counties laws, no human rights.
The second if you had 100000 show up and not pay tax, you would start changing your mind. The point was the laws for the country you build are established by you, not those arriving