Which are the default dimension of the Home wallpaper/background for the various Android screen configurations (small, normal and large screens with low, medium and high den
This article on the Android Developers' site shows the range of screen resolutions for each density.
I believe the wallpapers have to match the screen resolution and are not stretched. You can see this if, for example, you create a new emulator with a high screen density like 480x854. The default home screen background is centred, with large black bands at the top and bottom.
The WallpaperManager API indicates that you must use a PNG- or JPEG-format image, even if you use the setResource() method — the resource must be a Bitmap and so not a nine-patch or other type of Drawable.