Do you get an annoying prompt periodically on the Mac asking you if you wish to remain connected to the Internet? This is due to a setting on the computer, and can be turned off by doing the following:

For a Mac OS X system, open the Network pane of System Preferences. If a phone line is being used to connect, choose Internal Modem, and then choose PPP from the list of connections. If an Ethernet connection is in use which requires the use of PPPoE, choose Built-in Ethernet, and then choose PPPoE from the list of connections. Once the correct type of connection has been chosen, click the Options button; you can turn off the reminder here.

If this happens in a system running Mac OS 9 or earlier, open the Remote Access control panel and click the Options button at the bottom. Under the Connection tab, uncheck the box for prompting that the connection be maintained. This option is not set by default in Mac OS 9 and earlier.