The Company I am with gives the F/O the whole show from pre-start to shut down. The only slight exception is that the F/O can only abort the take-off on the Captains command. In other words when they are conducting a PF sector they do the lot.Oh almost forgot, Captains must do the Cat 11/111 landings also.
Personally, due to my past I am not completely in aggreement with the policy but they put the money in my bank account every month so I guess they can say how we play with their toys.
Have a nice day