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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?