Thank you, Erel.
The FIT mode will leave some space at top or bottom (or right and left).
If I have a background image with a circle inside, such circle will transform in oval if resized in FILL mode or remain a circle in FIT mode, but with some space at the borders.
The problem, however, is just in iPad compatibility mode (320x480 ratio is 1.5); the other formats are all very near to ratio 1.775 and there is no problem to resize.
Circles are still circles and there are no empty areas at the borders.
If you want a full-screen background image that is good for 320x480 and for 320x528, you have to ask your graphic guy for 2 different images, designed for the different x/y ratios; or, you can resize (in-app or externally with graphic tools), but you will see "fat" characters, logos and so on.
I can't understand why the compatibility mode doesn't offers a "native" resolution of 320x528 or 375x667 !
Both of them can be easily placed "natively" at center of the iPad screen, that has a bigger resolution.
The actual way is a "compatibility mode" that is not compatible with newer iPhones, but only with the very first 3.5" devices!
Add to this that many and many developers doesn't want to create their apps for iPad ! Mah... Apple rules.
Anyway, at and of the games, I'm going to accept background images with empty borders or fatten logos, depending on the solution adopted.
I just hope that the App will not be rejected for such silly problems.
Thank you, as usual, for you precious help.