Okay, as frustrating as it is to have you simply repeat your initial statements despite any arguments made to the contrary, it seems as though your point hinges on the distinction between personal and private property.
However, I don’t see how private property couldn’t be maintained as long as you have the ability to defend it. Hiring guards for instance does not constitute a monopoly on violence, since others can do so as well. In an anarcho-communist scenario, for instance, if the workers want to maintain control of the means of production after ousting the owner, they would potentially have to post guards as well, or the property owner could hire a bunch of mercenaries to take the property back.
The long and short if this is, I don’t see how anarchy would favor either the creation of capitalist or communist structures of organization. Most likely, there would be both, and survival would be a matter of who is better at organizing.