I have often mentioned game theory, rules, and the UN in the same sentence. Do not mistake this for a belief that the UN is of any relevance at all as a lawmaker in itself. Not only that, Australia would be my first choice as a world government, followed by the USA. The UN as a "government" is a toothless paper tiger and not capable of governing.
The set of treaties that have been signed by countries *does* determine the structure of the game and the moves each country can reasonably make. Thus, no matter what in theory the UN "decides", for instance on Iraq - the US being a security council veto member could not be stopped by the UN itself, but only by the domestic voting public that cared about what the UN decided.
Similarly with Russia in Georgia, China in Tibet, and in some way - Israel in Lebanon and now Gaza. The UN is important only in the sense of the importance of the individual treaties to the actions of various countries.
Thus several theoretically sensible annexations or merging of countries are very very unlikely due to the dynamics associated with how those treaties associated with the UN manifest themselves in Geopolitics.
Thus to consider entertaining possibilities like Australia annexing Pacific states etc., a new post-UN world order would have to be assumed first.