The novel's obviously of limited use for this question, since the family configuration is so different. It does say that several top Barzini and Tattaglia capos switched sides after the massacre, which could imply that some rump was left that did not. So maybe Michael just consolidated within what he thought were defensible areas?

The novel seems to link the name of the family with the name of its leader 100% of the time, so that could imply that Barzini had a son in line to replace him.