That isn't clear and its quite wrong... I can understand what you're trying to get at with regards to equity but as far as actual ownership is concerned its irrelevant.
You don't need 100% equity to 'own' the property... you are the owner when you're on the deed regardless of the size of the loan secured upon it. You get 100% of the rise in value of that asset because you own it... yes there may or may not be a liability linked to the asset but that liability is separate.
Of course you get 100% of the rise in value because the liability is fixed at the amount agreed at the beginning of the term.
Ownership is defined in various ways dependant on the context.