There's a book by Rothbard, I think it is his "The Ethics of Liberty", where he describes a set of libertarian principles and then how he thinks a society could be made based on those principles. What makes it interesting is that he tries very hard to not have to compromise those libertarian principles, following them even if they go to some places he agrees are pretty dark and trying to explain what would prevent that from happening.

He covers the issue of parents having to care for children and concludes that they would not be legally required to do so. Go ahead and go to Vegas for a weekend and if the baby can't figure out how to survive on its own that's not legally your problem.

His argument for why this would not lead to the large number of baby deaths by neglect that probably most people reading this are sure it would is that adoption would not be regulated in his ideal libertarian state. There would be a totally free market in babies. You could make a lot more than you'd ever win in Vegas in a weekend by first putting your unwanted baby up for sale.

I don't find his arguments very convincing, but it is interesting if you treat it more as an intellectual puzzle than how you would actually set up a society.