How do I stop Ubuntu from automatically dialing out?

I noticed my broad band router reports "DOD:triggered internally" soon after I click on hang up.

Dell 1520, Ubuntu 10.04. Presently connected to DLink 704 router by ethernet. Router is connected to USR Faxmodem. I usually have other things connected, to the LAN, so while disconnecting eth0, keeps Ubuntu from automatically dialing out, it prevents me from connecting the other things on the LAN.

I have Thunderbird and Firefox and the update manager configured to not automatically look for updates.