How to stop system logging!!!

I have a linux box that does ip translations and the hard drive fills up with dhcpd.leases.xxxxx files ubtil the box shuts down.How can I turn off the logging of the ip leases. Can you give my steps on how to do it. If I delete the dhcpd.leases.xxxxx files the box will run for a few days and then the hard drive fills back up. I don’t need any type of logging on this box. I think the logging file is syslogd and klogd but I am not sure as to what to do to these files. Please help!!!! Thanks Gary!!!!