Random Drive Mappings

Sounds as though this share has been mapped through network nh, and the checkbox reconnect at login has been checked. Simply going to network nh and disconnecting this drive should work. You can hide network nh from your users using policies.
bestof luck

Is it computer specific or user specific. If it's not the logon script then it could be something running in startup on the computer. Or it could be something odd in the user profile...

I think the first step should be to find out whether it's the user or the computer...

Then an analysis of the startup process, including the contents of startup, HKLM\Software\Microsoft\Windows\currentversion\run* might give some information.

Should probably also check autoexec.bat for any odd net use calls.

This was a known problem with NT Workstation SP 4 or older. If you have not done so, upgrade to SP5 or 6a.

Also, if you have Office installed, FindFast can cause this behavior. Findfast was designed to create an index of all office files so that they can be more rapidly accessed when you choose File -> Open from within an Office application. One of the negative side effects is that if it finds a shortcut on your harddrive that points to a document that is stored on a network share, it automatically maps a drive to it. I have found that FindFast is more trouble than its worth, so I stop it. Delete the FindFast shortcut from the Startup Folder. Then go to Control Panel -> FindFast, highlight each Index and delete it, then from the menu choose Close and Stop.

Known problem with findfast.
disable find fast to start up automatically, typically it's found in the startup folder.

Success.