http://verify.abuse.net/relay.html
This site tells me, when I enter my domain name, that my mail server appears to be an open relay. In addition, when I register for abuse.net and try and get it to send an e-mail to me, that e-mail successfully arrives. This would suggest that my host is acting as an open relay!
As cPanel is what writes exim.conf (I make changes, they're liable to be overwritten), I'm guessing it's cPanel's responsibility to tighten this up. Why on earth is my host acting as an open relay? How can I stop it with cPanel?