UN/LoN-esque organization after World War III

The League of Nations were created after World War I and was disbanded after World War II due to ineffectivity.

The United Nations were created after World War II to make a better League of Nations and it wasn't disbanded after World War III because latter didn't take place and its possibility was undone by the superpowers themselves, not the UN.

So what do you think would be the fate of global international organizations of this style after World War III? Another "more perfect United Nations"? The UN disbanded without surrogate? The UN stays what it was before the war? Any other ideas?
 
Posabilities:
1) The new world intergovernment body has the power to enforse treaties and direct military forces to trouble spots in defense of member governments. Financed by its own bank.
2) the new world government, post WWIII, is the tribal elders of the suvivors sitting around a campfire debating the issues. Like whether to migrate south or follow the river; should Bob and Mary be allowed to keep that mutated cow or should we eat it? Stuff like that.
 
Given the entire point of the UN was to prevent WWIII, it seems there is a strong chance that the conflict might convince people the idea is impractical and ineffective. Given the choice between abolishing any major IGO or strengthening it, it is likely that there would be enough opponents to the idea that the new IGO would unite a number of key players but leave out a large, skeptical part of the world.
 
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