How is a private university taken over by the state? Is there only one way to do it, or more than one way??
A superb question D&Dfan, which may be a future matter that will garner more attention. I do not profess, by any means, to be any kind of expert on this, but do have some comments.
Deviating somewhat, last year, when the Supreme Court held that via eminent domain that governmental entities can take private property (land) to be used for private purposes if viewed for the public good, is going to have a lot of future implications unless legislative bodies enact on the issue otherwise. Of course, no situation has emerged yet whereby a private higher education institution has been involved. This scenario is focused on private to private transactions, but theoretically a situation could emerge whereby the state is a facilitator in forcing a transition. Be that as it may, I doubt we would see an exchange for the same general purpose between private educational groups.
Prior situations, in multiple states, have resulted in former private higher educational institutions becoming public. These, for the most part, have been secular colleges who have requested state take-overs by their Boards of Trustees due to institutions not being able to maintain financial stability as they currently exist. Colleges functioning under the umbrella of governing religious bodies, would not have the independence to seek state ownership on their own. Of course, the state is under no obligation to accept or maintain the institution as it has traditionally existed. Relieving prior debt may be a negotiated matter in the state assuming ownership. The maintaining of the current faculty and administrative staff may not be automatically assumed. Particularly, the state will usually change administrative staff deeply. Faculty may need to satisfy new criteria as well. Differing states have varying bodies, legislative committees, and procedures for incorporating previously private institutions. While legislatures and the state's governor would always be involved to differing degrees in such decisions, state colleges come under varying governance schemes depending on the state involved. Some (state college systems) function more independently than others. Approval and sponsoring processes are always layered with state agencies.
The University System of Georgia is one state governmental agency that has a history of absorbing a former private college. For instance, Gordon Military College (Barnesville, GA) in 1972 entered the system and re-named Gordon College. In South Carolina, Lander University (Greenwood) was previously private and is now state affiliated.