No, not using property, or not even paying the taxes on it, has no effect on your ownership of the property. However, in the event of a sale of the property, he could likely get a court (if you and he could not voluntarily agree on the distribution of the proceeds) to  award him more of the proceeds to compensate him for having paid expenses you did not--e.g. award him an amount equal to the taxes he paid. Or he could potentially sue you to force you to compensate him for the share of taxes which you should have paid.