They would more than likely fly Airbuses, seen as thats where their fleet is headed + all the cockpit commonality stuff.
How exactly would asylum seekers find it easier to get into the US? EZY is a point-to-point airline, which means that any incoming asylum seeker would have to be completely checked-out at a UK airport, before checking in for their UK-USA EZY flight. Therefore, they would end up at British immigration.
Its likely that they will see if some other operator (such as skybus?) can make it work, and then take over them and call it easyAtlantic.
easyBizJet is a interesting one though.