George, WikiTree does not have private trees (or public trees, for that matter). Here there is only one single tree for the entire world. When you get far enough back, many of us share the same ancestors, but the idea here is that we all collaborate - working together to find more information that is more accurate than any one person could do alone.
If we ever discover that there are more than one profile for the same person here, we are required to merge them - this combines them into one single profile, retaining all information that had previously been in both.
WikiTree does have privacy levels for profiles, but these determine what information in a profile is or is not displayed to the public. Open profiles and public profiles both display everything that is there. The difference is that open profiles can be edited by any WikiTree member while public profiles can only be edited by profile managers and members of the trusted list. Private profiles can, if the manager chooses, display the biography or family tree or both or neither publicly. These, however, are privacy levels determined for each individual profile and have nothing to do with entire branches of our one single huge tree.
If this has not answered your question, please clarify what it is you are asking so that I or another member can help.
