Well I always hated it when IE opens up after the game closes because it happens a lot when the servers are full and you try to log on over and over, so heres a solution
For Internet Explorer:
Go to C:\Program Files\Internet Explorer and rename the file IEPLORE.EXE to something random, like maybe IEXPLORE.old. Now KO will not open IE when it closes since it can't find the .exe. This doesn't edit the KO client in any way so it does not violate the ToS.
To do this you need to have file extensions for known file types shown. If your extensions are hidden (Windows XP default IIRC) you need to show them. Go to Tools | Folder Options in Windows Explorer and choose the View tab. Uncheck the box next to 'Hide extensions for known file types' and click OK. Now you can proceed with the fix I outlined above.
Best of all, Internet explorer will create another .exe after you do this called iexplore.exe (all lowercase). Just update your IE shortcut to point to this file and you can browse normally with KO still not opening the page when it closes.
For other browsers, just navigate to its install directory and rename its respective .exe and this should work.

Thank me if this helps you