I have been experiencing this rather strange "mystery" or "ghost" tab that auto opens upon starting SourceTree. If you wait (forever) the tab eventually finishes loading and it becomes apparent that the repo is for my C drive.
I have found no way of fixing this. I have uninstalled SourceTree, restarted my computer, reinstalled, followed by yet another restart and this mystery repo continues to show up.
I have followed guides online to do a forced cleanup, which also failed to remedy this problem.
Thank you to anyone who can help out.
To attack this from the other end...
Did you intend to make a repository of your entire C drive?
If not, make sure you can view hidden files and folders, then look for a .git folder in C:\. Delete it.
You may also need to follow Balazs' steps to remove a stored bookmark.
(Sorry in advance if any of this is trivial.)
If this does not solve your problem, it might be that the place where ST stores the state of the tabs is not writeable by ST. (Unfortunately, I don't know where that is.)