SP2010: Custom logout page
What happens is, you choose to logout, get sent to the logout page where you are prompted to close the page, which you probably don’t want to do, then you click the link “go back to site” which on doing so, logs you back in!
If your authentication provider (ADFS, IDM, etc) has a logout page, then you probably want to redirect them to that. Or if you want to customize your own logout page, well more power to you!
To change where the logout link brings you to, you need to modify the Welcome.ascx control template.
Browse to /14/TEMPLATE/CONTROLTEMPLATES and edit the welcome.ascx file.
You can add a property called ClientOnClickNavigateUrl to overwrite where the “log me out” link brings you to.
Once you save this control and refresh your page, you will have a new logout destination!