From Wikipedia: “elimination of the state and the provision of security from aggression against person and property by the private sector in a free market.”

The latter is essentially a proto-government. The contract between individuals and their private-sector security will very quickly come to resemble paying taxes in return for enforcement of a code of laws. Then the contractees will want the ability to change those laws. Perhaps they will decide by majority vote. Now you have democracy. So “anarcho-capitalism” seems nonsensical.

http://en.wikipedia.org/wiki/Anarcho-capitalism

Of course even Ayn Rand saw the problems with this:

“[S]uppose Mr. Smith, a customer of Government A, suspects that his next-door neighbor, Mr. Jones, a customer of Government B, has robbed him; a squad of Police A proceeds to Mr. Jones’ house and is met at the door by a squad of Police B, who declare that they do not recognize the authority of Government A. What happens then? You take it from there.”

http://stason.org/TULARC/ideology/anarchy/11-c-The-minarchists-attack-on-anarcho-capitalism.html