Murray Rothbard the man who invented the idea of Anarcho-capitalism said himself that they are not anarchists, saying "we are not anarchists, and those who call us anarchists are not firm etymological ground, and are being completely unhistorical" Because, all anarchists had socialistic elements in their doctrines and possessed socialistic economic doctrines in common" This is from his article called "Are Libertarians 'Anarchists'?"
Murray Rothbard is WRONG. Not all anarchists hold socialistic economic doctrines. That's like saying all communists are Russian.
In conclusion, it is not anarchism, you are just a capitalist. And what you will have on your hands is what we have today. Corruption and tons of power to the rich.
Do not use the word "power" if you do not understand what power is. The rich are "powerful" because they are able to bribe the government. THIS is why we have anarcho-capitalists. The rich have very little power when there isn't government to bribe.
That is anarcho-capitalism. Anarchism is a stateless society, and anarcho-capitalism is a stateless society that operates off a free market. That is literally a form of anarchy.
If you support a free-market that exists without government, you're an anarchist, and anyone who says otherwise is misconstruing the definition of anarchism.
Capitalism, socialism, and communism all have to do with economics. They can all theoretically be anarchist, or totalitarian. They can all be a democracy, or an autocracy.