When I sign out of Sharepoint 2010, I close my browser. When I attempt to go back to sign-in, I see that I am already signed in. All of my browser instances are closed. This is using Windows Authentication, but I usually have to sign-in when logging in for the first time to my machine or deploying a webpart.
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I’m not sure I see a question here.
What I believe is occurring is SharePoint is delivering a cookie to your browser that is authenticating you. To test, you can go into your browser settings and delete your cookies and then try to access the site again.