Does the Private Company Take Ownership of the Park?

No.  The parks and all the facilities remain the property of the public entity.   The park operator merely signs an operating lease, with strict rules, wherein it operates the park, keeps the fees paid by the public, and pays the state a “rent” based on a percentage of the fee collections.  Even when private companies invest in facilities, like this store building and cabins, these facilities become the property of the public at the end of the contract.