I'm currently using FMP10 on a new Core i5 iMac - I had this same issue on a G5 iMac too.
Most of my databases open in the same window size and position they were last closed in. But I have two databases which I normally wish to have open together so that i can migrate records from one to the other - but they both open to fill the entire screen of my Mac. I resize them, and close them resized, but it makes no difference - next time I open them they go full screen again. (Both databases were cloned from one original, which is why they both have this behaviour).
I had a look in Preferences, but these are now all application specific only. How can I get these databases to open with the window size and position they were closed in?