My installation of iTunes 12 would not remember my window size or position, and a splash screen would flash when the app was launching. I tried everything and could not get it to work correctly. Apple won't allow you to remove iTunes as the OS requires it, so I was left floundering.

I found the fix by accident.

1. Go to Preferences - Store
2. Check the box for "Share details about your library with Apple."

As soon as I did the above, the splash screen went away and my window size and position is remembered.