Once you finish residency, you go looking for a job just like any other Joe Shmoe. Hopefully, you've found one before you've finished residency, actually. We had this question answered pretty recently IIRC. Partnership in an EM group is the same as partnership in any other professional assocation of physicians. The difference in EM is that a significant portion of EPs are employees of corporations that hold contracts with hospitals rather than partners in a group of equal colleagues.
Where you finished residency may have some bearing on where you work right out of residency, but it's more important that your faculty like and trust you enough to give you a strong reference letter when looking for a job.
Once you're out and working in the community, where you went to residency is all but completely irrelevent. What matters is how your colleagues felt about you and how well you performed. Again letters of reference are key, particularly from your medical director where you worked or from hospital adminstrators as well if you were the medical director. Prospective employers will also often ask for a letter of reference from a charge nurse or nurse manager at a hospital you've worked at. So don't be a pompous ass and piss of your nurses, because it will come back to haunt you.
I'd also add that looking for a job in EM is like looking for a job in most other fields. Networking is key. If you are trusted and liked by someone who is in turn trusted and liked by the person doing the hiring, then you've got a definite advantage.
