Debian, minimum to send mail but not receive any

nullmailer

(source)

• install

apt-get install nullmailer mailutils

• Fully qualified domain name: yourCurrentServer (does NOT to have be fully qualified)
• SMTP server: imap.yourdomain.com

It should work now, but you can tweak inside /etc/nullmailer/ the following files:

• inside /etc/nullmailer
  • adminaddr - target mail (not understood yet by me, sorry)
  • defaultdomain - source mail (so the sender not root@server but root@server.domain.com)
  • remotes - target login