In our British short-haul airline, for a RHS take-off (on the 737), the F/O sets approx 40%, Capt calls “stable”, then F/O presses TOGA and removes left hand from thrust lever back to the control column. Capt then covers the thrust levers until V1 which are normally moved to the take-off thrust setting by the autothrottle.
The Captain will be monitoring the engine instruments & aircraft performance throughout the take-off roll whilst the F/O is concentrating on flying the aircraft, he (the F/O) only looks in to cross-check the ASI calls. Therefore the Captain is better placed to make the go/no go decision than the F/O and, as he is guarding the thrust levers he can immediately initiate the procedure if required. The F/O’s actions in an RTO include keeping the nose-wheel in contact with the runway and the wings level, both of which require both hands on the control column, which is where they are.
The procedure is slightly more tricky for a LHS take-off where the Captain flies with the left hand and covers with the right, but with his experience this is not a problem. The F/O will be making the speed calls, watching the engine instruments and is poised like a coiled spring to assist with the control column actions in the event of an RTO. Again the Capt makes the call as his hand is on the levers. Note that the speedbrake is on the LHS of the throttle quadrant so would be more difficult for the F/O to deploy. This system works fine in the sim and although I have not yet had one for real, I was as happy with it as an F/O as I am now as a Captain.
“STOP” is the biggest call you will ever have to make in your career and it would not be fair to the F/O or the pax to delegate this away from the most experienced crew member.
As an aside, Tobias said
“First, if you flex to minimum thrust on every take-off, you are putting yourself at very much greater statistical risk of a disastrous late reject”
It is worth mentioning that using a reduced thrust take-off will put less stress on the engine thereby reducing your chances of having the engine failure in the first place, but I am sure this has been discussed elsewhere at great length.
S & L