Hello Joe,
Just wanted to add a bit to what Mark mentioned in the reply. There is usually a transition period of 48 hours. During this period, some of the servers worldwide will send mail to the old host. So just keep their (old system's) login passwords handy. If you don't see some mail here, it will be there.
If you use a webmail method using domain name, example
http://yourdomain.com/webmail, then keep an alternate way to access the same as well (such as
http://youroldhost.com/webmail)
I don't wish to confuse you but we at eukHost would like to ensure you have a smooth move.
All the best!
Regds
IJ