i have been dealing with setting up a mail server, lately. debian seems to have a preference for exim. most of the mail admins i know also support this. so i had a look at this.
as it always happens to me, i start with a not so easy scenario, but after some figuring i got it, mostly by following this guide: Configuring Exim4 and Courier IMAP under Debian GNU/Linux.
what the article does not say (and might be common knowledge — i will still describe this here for anyone who does this the first time) to have mails addressed to domain xyz.com be sent to the appropriate mail server, there needs to be a so called MX entry (mail exchanger). See also section 5 of RFC 2821.