tke71709, that’s because when you use the toolbar it enables the search history function of Google. Disabling the software doesn’t stop the web based service because it functions while your logged in, it’s not something built into the toolbar itself (it runs externally via Google’s web portal). You can easily turn off search history by logging into your account and going to the search history section, it’s not rocket science and it surprises me that you weren’t aware that it existed.
Whether I can do it is one thing, whether your average person can do so, and whether, ethically, you should stop doing something once a piece of software is uninstalled is another question entirely.
If you install a piece of software, and as part of that install I agree to allow you to do something else (e.g. monitor my Internet usage like the Google toolbar does) then when I uninstall said software you should stop doing that IMHO.