Well as far as I can tell, from the rules, your domains are defined by what your people believe more than any innate ability on your part. Whatever they associate you with, you gain power over as it is their belief which sustains you.
That said, a formal contest between you and another god (or even a fight to the 'death') using the domain over which you are fighting exclusivly would be interesting. For example, if you're fighting over the War domain perhaps a small wargame, winner gets the domain added to his portfolio.