In the RAF, we trained both pilots of a VC10 to be sufficiently competent to execute a rejected take-off correctly.... Handing over control during such an event is UTTER nonsense until at a standstill and highly dangerous with the danger of a "Who has control?" event - but that's what most airlines seem to advocate.
The call would be:
ABORT! for those failures which would necessitate rejecting a take-off. That call could be made by the PF, PNF or FE. The Capt would confirm the reject by closing the throttles. PF would apply max braking and steer to a halt, PNF would extend full speedbrake and full reverse thrust. Reverse thrust would be deselected when ordered by the PF. When stationary (and NEVER before), the Capt would take over control by announcing "I have control" and would apply the parking brake. The Co-pilot would retract speed brakes and extend flap to approach (in case overwing evacuation was required). Then the Capt would request "Reason for abort?" and decide whether to taxi clear. We were fortunate enough to carry a navigator who would check the brake energy absorbed and indicate in which zone (Normal, Caution or Danger) the brake temperature was likely to be; the Capt would act accordingly.
We had the same rejected take-off drill from zero knots right up to V1 - none of this above or below 80 KIAS nonsense. Crews normally practised rejected take-offs in the simulator at least once per month both as PF and as PNF...
Above V1, the only call would be "FULL POWER" if reduced thrust had been set for normal take-off.
Rarely did crews screw up a rejected take-off in the simulator (after completing type conversion) - practice made perfect!