The person who purchased the competition is the owner of the competition. Ownership can not be transferred to someone else. The owner can appoint an Admin. An Admin is someone who administers the competition. Both the owner and admin can answer questions from the players, remove people in the ladder, set Rules, Prize and other competition settings. Usually the Admin is the primary point of contact for ladder related questions. The role of the Admin can be assigned to a different player.
The latter can be done under My Competitions, Edit, click on current Admin, select new Admin from list, Done