The last server migration (which was when SE created new servers and allowed people to join them with their current character), you applied to switch servers. Any person that left a certain server went to a specific server. For instance, those that left Cerberus all went to Hades. At least, I think I remember it that way. Might have been 2 possible servers you could end up on. As for the new servers, they got people from many different servers. It didn't act like "I don't like Cerberus, I want to go to Fairy."
You were able to keep all you items with some restriction (for instance, you inventory was carried over but nothing in your delivery box).