If an engine fails after $V_1$, how long does the copilot remain in control if he was the pilot flying? What is prioritized before the captain taking control of the aircraft?
The operating procedures for the four airlines I worked for (2 commuters and two 747 carriers) all called for the flying pilot (which would be the first officer if it was their leg) to retain control of the airplane until all relevant checklists had been accomplished.
That said, it is, of course, the captain's prerogative to take control at any point. That would, I think, be very unwise to do in the case of an engine failure during takeoff unless the first officer was really screwing up.
The greater workload in the 747 during emergency/abnormal procedures lies with the non-flying pilot and the flight engineer (old 3 man cockpit 747-100s and -200s).
The recommended procedure at my last two airlines was, if the captain was flying at the time of the failure, to hand control to the first officer after all relevant checklists had been completed, to thus enable the captain to give his full attention to how best to proceed.
My personal and observational experience is that there is little difference between captains and first officers at the 747 level insofar as control manipulation during go/no go situations on the runway in simulators. In fact, I could point you to an accident resulting in the total loss of a 747 when the flying pilot was the Captain, and he elected to abort 30 knots after $V_1$, thus insuring the aircraft would leave the runway.
In airline operations, both pilots are trained to handle engine failures at any point during the flight, including during the takeoff.
As far as who actually flies when it happens, it is a matter of the airlines SOP's and could be different from airline to airline. In general it is safer for whoever is flying when the engine fails to continue rather than attempting to transfer the controls. After an engine failure during takeoff, the aircraft is in a relatively unstable condition which often needs high control forces and the person flying has already figured out how much control pressure is required to keep it flying like it is supposed to.
The captain is always the final authority when it comes to the safe operation of the flight though, so if he felt that it wasn't going well, he could take over at any point. Many captains actually prefer to have the first officer fly during abnormal situations like this because they can then "oversee" more effectively without having to focus so much on actually flying the airplane.