This has been asked here: How to persist JavaFX GUI State? And has the tag javafx-2. But no answers.
Gonna ask again and put in more tags.
I'm looking for something like what was done in JSR 296: Swing Application Framework where the demo application remembers it's window size, location etc. E.g if the user maximized the window, and then closes, opens the program again, the window is maximized.