You can clear cookies manually to get logged off from Hotmail. Hotmail leaves a lot of cookies behind anyway even if you log of. You can look for live.com and passport.net and msn cookies if you w3ant to cleanup. In the past it was necessary to enable third-party cookies to get logged of properly, but that is no longer necessary for me and enabling third-party cookies will give you a lot of extra cookies from all kind of ads sites.

thanks I finally got the problem cleared up - remember to do a refresh after clearing the cookies

This didn't work for me. Still have the problem.

(but thanks for the tip about no longer having to accept third-party cookies in order to use Hotmail: that's good news)