First, just a side comment... never ask something in caps. Long gone are the days of caps only input, and it looks like you are yelling at us.
Next, what history are you refering to? Internet Explorer? Mozilla? Cookies? There are a bunch of things that you would need to do upon logoff to ensure your objective.
A better idea though would be to password the computer so that only you can access it. Or, if you are doing illegal / immoral things, perhaps you should re-think your computer uses. It would be A LOT easier to physically secure the computer so that no one else can use it except for you.
P.S. If someone wants to track you, they can always pull your DNS logs, or plop a network sniffer on the computer. We used to do that all the time to kids in a computer lab, and made a point of educating them with letters to their parents and detention. It all depends on how much work the administrator wishes to do, and what scripts he/she comes up with to automate the process.