Doms never own a sub.They invest their time and ideas in order to gain respect of their subs.In this process,they develop so much trust with their subs that they both feels a deep connection between their hearts.
After this phase of their relation,sub completly trusts her dom/master,then she do everything the dom asks....and to everybody ,my friend,it appears as if the dom owns this sub.
Hope you dont find this answer ridiculous....lol.