The first five books, I think, are in the public domain.
I’m not sure what you mean since Disney itself undoubtedly took advantage of the public domain status of the first book. Disney holds rights in its own adaptation of the work to the extent that it created any new expression, and controls its own derivative work, but has no exclusive rights in the underlying work and can’t stop anyone else from making another one. As shown by the Asylum’s production, you’d have to have resources on Disney’s scale to do justice to it.
Well I am referring to Disney’s well-known aggressive stance in protecting its properties. It is possible to protect stuff even if it is in the public domain, as the Burroughs estate has done in the past. For example, I wrote a review of a lame-brained Italian B-movie called Thor the Mighty Hunter. It had ORIGINALLY been called “Tarzan the Mighty Hunter” but the Burroughs estates’ lawyers got wind of it and forced them to change the name to “Taur the Mighty Hunter.” “Tarzan” was in the public domain at the time, but the Burroughs estate got around that by trademarking the name Tarzan so no one else could use it, despite the fact that the work itself was in the public domain.
(I’m not sure why they changed the name to “Thor the Mighty Hunter” as there is nothing remotely Scandanavian about the movie, which is clearly set in the Bronze Age in the Middle East – not exactly Tarzan’s stomping grounds, either.)