Communism is more anarchic than capitalism, because it definitively has no precise point of rule. There is no government controlling means of production. An association of people mutually control all things.
Capitalism on the other hand, requires there to be protection of individual property rights (which has got to come from somewhere), as well as that it allows people to gain infulence by amassing more wealth than others.
Of the three, socialism is the least anarchic, however it is also the least defined in terms of a model. Some argue for anarcho-socialism, but I honestly don't think the concept makes much sense. Socialism essentially requires and overseeing body to regulate and provide common goods.