What reading did you do in regards to it blowing over the world? Uranium (or Plutonium) is a very very heavy element, so it wouldn't likely blow very far. Now, the cooling material that nuclear reactors use are often light (and noble gases), so if there is an issue with a reactor, than I could see that blowing around (like what happened with Chernobyl), but those coolants are not used in nuclear weapons. If they get a fission bomb (like the bombs dropped on Japan), the material should fall to the ground pretty quickly. Like Japan, it didn't spread very far (on a global scale). If it is a fussion bomb (like an H-bomb), the helium that comes from it, rises up and out of our atmosphere (because it is so light), so it won't spread either (though the neutrons will make just about anything radioactive in the vicinity).

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