The international Aikido Federation is a blanket federation in which many (but not all) of the Aikikai dojo are under.
http://www.aikido-international.org/...pper&Itemid=32

The IAF was founded by the Doshu.To be a member of the IAF, or any of it's member nation federations you have to be affiliated by Hombu Aikikai. The president is the Doshu.
The IAF presently has a rule that only one federation from each nation will be recognized by the IAF to represent Hombu in that nation.
To have a school recognized be any federation under IAF you must have lineage through that federation, and possibly its Shihan.
The IAF's purpose was to help give the world access to high ranking Hombu instructors. The Uchi Deshi of O'sensei are the founders of many of the Member nation's Federation. The goal was so that every country would have access to the Aikikai Shihan.
The goal is to not just spread Aikido, but good Aikido.

Your school won't have affiliation to any other dojo outside of the IAF, but if will have lineage with any other Aikikai style dojo. So long as your black belt is through Aikikai Doshu, it will be recognized as a belt in Aikikai. (You can't expect Yoshinkan or Suenaka schools to recognize an Aikikai belt either A black belt in Aikikai doesn't mean you are proficient in other styles Aikido, it means you know Aikikai style Aikido.)The same can not be said for kyu ranks however. Kyu is only recognized if it within the IAF, other school's kyu is not recognized because they might have different standards for belting.