As the host to detect spammers among customers?

enable SMTP authentication for users and analyze logs of the mail server with the withdrawal of top of the most active usilitelei emails per hour for example. As an option — define boundary values and shove into the monitoring system

Better to prevent spam and not to look, because in many cases the user simply hacked and does not know that his account sends spam.
Spam can be sent in two ways
1) installed the mail server (e.g. exim)
2) Directly from php, perl, etc.
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To prevent spam you need
1) To prevent sending a first option to set limits for users, if you have exim, similar to this. Of course, follow the instructions, don't, just watch there realized
2) Close the iptables means all outgoing connections on mail ports to all except a user running exim

To prevent spam — the best way:
1) to capture this moment in the customer agreement( if not concluded in writing, in the offer on the website)...
2) before the institution of a new client is talk to him and discuss it..