Hi Peter,
In ArcGIS 10.1 and 10.2, when you author your projects using Mobile Project Centre, you need to add basemap using option "Browse for Basemap-> Already deployed to Device". So the AMP file have a reference to this basemap.
On the device itself, you need to use "Settings->Application Settings->Additional Basemap Folders" to specify where your basemaps should be attached from. And you will need to copy the basemap cache to this folder. After this, you can use same basemaps for multiple projects.
Cheers,
Vish