The radical libertarian tradition holding that every legitimate social function — including law, adjudication, policing and defense — can be supplied by voluntary exchange, and that the state is not a necessary framework for markets but a coercive monopoly competing with them.
Murray Rothbard founded the modern form by pushing two inheritances to their conclusion. From the Austrian school he took the argument that monopolies allocate badly and that the state is a monopoly like any other; from natural-rights ethics he took self-ownership and the non-aggression principle, concluding that taxation is theft and conscription slavery regardless of the good either might fund. Man, Economy, and State (1962) and The Ethics of Liberty (1982) set out the system; For a New Liberty (1973) made it a program.
The tradition divides on why the state should go. Rothbard's case is deontological — the state is illegitimate whatever its results. David Friedman's The Machinery of Freedom (1973) is consequentialist, arguing that competing private agencies would simply produce better law, and explicitly declining the rights argument. Hoppe took the tradition in a more socially conservative and much-disputed direction. These are different enough that adherents of one frequently regard the others as having conceded the argument.
Its most-cited objection comes from within libertarianism: Nozick argued in Anarchy, State, and Utopia (1974) that competing protection agencies would consolidate into a dominant one that behaves as a state, so a minimal state arises from anarchist premises without anyone violating rights. Critics outside the tradition question whether private law could produce anything but the law preferred by those able to pay for it. The position remains a minority one but its influence on the wider libertarian movement, and lately on crypto-adjacent political thinking, has grown well beyond its numbers.