In the company I work for The Captain is always responsible for initiating a RTO and becomes the PF if not already.
Capt PF - Capt sets approx power, calls "check power", removes hand from thrust levers to allow PNF to adjust.
- PNF adjusts thrust levers as required, calls "power set". Capt takes control of thrust levers again.
- At V1, Capt removes hand from thrust levers.
RHS PF - F/O sets approx power, removes hand from thust levers and calls "check power".
- Capt adjusts thrust as required and leaves hand on thrust levers in preparation for reject.
- At V1 Capt removes hand from thrust levers.