How can I remove an old server name from Windows XP & Windows 7 computers so that they will no longer try to resync with the old server?

How can I remove an old server name from Windows XP & Windows 7 computers so that they will no longer try to resync with the old server?

We have just migrated a Server 2003 SBS AD network to a Server 2008 AD network.

All computer, user names, share names, etc. are exactly the same as they were before.

The only difference is that the new Server 2008 SBS server has a different computer name than the old Server 2003 SBS server.

I have been able to set up the Windows XP and Windows 7 client computers to properly synchronize their offline files with the new Server 2008 SBS.

The problem is that they also still try to synchronize with the old Server 2003 SBS.

What do I need to do to remove the old server name from Windows XP & Windows 7 computers so that they will no longer try to resync with the old Server 2003 Small Business Server?