Nope, there is no rule about it. Admin can do what he want :) That's why fansites like TibiaMisterios, TibiaTV made only one contest in its "career". Ex-fansite TibiaGuias made two contests. If owner of the fansite wants to keep fansite item really rare, he can do it by not giving it to anybody. He can organise fansite item conest, but he doesn't have to. He can design it on his own and be the only person who owns this item. It's all up to him. Items like Citizen Doll or Shield of Endless Search were create by admins. IMO it was bad idea xD
That's why I repeat so often when I see crying how hard is to obtain 4000 poins on TibiaQA - that ppl should be thankful that it is possible to get the Omniscient Owl, because admin could keep it for himself and doesn't care at all.