We’ve dug up a handful of new details on Apple and Motorola’s iTunes partnership, which the two companies announced late Monday. The New York Times reports that the new version of iTunes that will ship on the phones will be called “iTunes Mobile Music” and that iTunes users will be able to transfer a dozen to a few dozen songs to their phone. Apple CEO Steve Jobs said he called Motorola CEO Edward Zander soon after Zander took over in January to suggest that the two companies work together on the project. According to Forbes, Jobs and Zander had finalized the deal only hours before yesterday’s announcement. And although iTunes will be the default jukebox on future Motorola phones, the deal is not an exclusive partnership. Finally, The Register points out that Motorola’s phones will become the first devices not produced by Apple to support its FairPlay DRM technology.