Imagine that if these companies that produce law and protect people are 1) No longer confined to any particular territory and 2) They have to attract customers rather than forcibly extracting money from them. Then you have the same anarchic world where these companies have to interact with each other but customers are free to choose who they want to go with and what level of service they want. The companies have great incentive to co-operate with each other. In fact much more so than governments of today, because governments of today can steal vast amounts of money and force people through threat of jail to obey them and kill for them if necessary. Those dangers don't exist in a voluntary society.
Actually, what you suggest boils down to having several states in the borders of one...

I don't think this is ever possible, but if it were, one of these "states" would eventually crush all the others and usurp the power. What would stop it from trying?

In any case this is not anarchy...
