You can't really make it *THAT* much smaller, so just turn it into a function, instead:
function popup( )
var winOptions = "toolbar=no,menubar=no,location=no,scrollbars=no,resizable=no,"
+ "width=" + screen.width + ",height=" + screen.height;
window.open("ExitWindow.html", "partnerSite", winOptions);
<body onUnload="popup( );">
Hope you realize that this is indeed a *classic* popup, of exactly the kind that many people's popup blockers *WILL* block. Depends on how strict they have their settings.
Oh...and I'm not sure screen.width and screen.height work for all browsers, but it won't hurt to try them.