rsync does not send emails, so something else wrapped around rsync is doing it. I'm assuming this is a cronjob calling rsync. The cronjob that runs rsync generates output on stdout. By default, cron then mails that output to root.
So first, find the cronjob that is running rsync. Places to look:
run crontab -l as root
Once you find the cronjob that calls rsync, try running it manually on the command line. You should find that it displays output that matches the emails you are receiving.
Next you need to redirect or suppress that output. In the cronjob, you can do something like this:
* * * * * /usr/bin/rsync blah &>/dev/null
to suppress all output. Alternately, change the rsync flags you are using to eliminate output, or redirect it to a logfile (but don't forget to then set up rotation!).
Another troubleshooting idea: include the headers from one of these emails in this question so we can examine them for clues.