First off the carrier can not assign fighters from inside the POS shield. He needs to poke his nose outside the shield to launch them.
The bandwidth does not matter for fighter assistance, but you can never control more drones than your skills or ship allow. For most ships this means that if you have not launched your own drones you can receive assistance from up to five fighters. The pilot will assume control of the fighters in much the same way is if they were his own drones, and they will follow him through warp etc. If the fighters are attacking a target and it warps off, they will follow and continue the attack.