The AppleScript Studio Workshop

Found a useful posting at Coding AppleScript on centering windows in AppleScript Studio.

 
tell every window to center

I used this tip to figure out how to automatically center my splash window when the application first opens:

 
on will open theObject
	if the name of theObject is "homeWindow" then
		tell theObject to center
	end if
end will open

This gets called before the window displays.