Took me two years to think of this so I thought I'd post it. I doubt K2 will bother to code around it since it only wastes their bandwidth anyway opening the damned site every time we dc/log out.
For Internet Explorer:
Go to C:Program FilesInternet Explorer and rename the file IEXPLORE.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.
Sorry if this has been posted before, I just did it this weekend so I thought I'd share for those of you still suffering from that damn site opening every damn time KO closes.
Added Konnko's contribution to the original post:
"Ok guys I found a solution for those who still keep getting IE popping up after deleting iexplorer.exe or renaming it.
All you need to do is to delete the file iedw exe and IExplorer.exe from IExplorer folder. The iedw recognises all crashes on IE so it keeps making IExplorer again and again... It makes the iedw.exe and IExplorer.exe again after you log out the first time but still doesnt open IE afterwards."