LHS only...
Where I work, PF advances the thrust levers, then when thrust is set, the Captain takes over. At V1 the Captain removes his hands until safely in the air and at V2 + 15 - 25 when PF should put their hands back on them.
The reasons for this are that in the event of a reject the Captain automatically takes control so there is less time having to swap hands on the thrust levers, and in the event of a failure after V1, the temptation to close the thrust levers is removed as hands are no longer on them.
That's just where I work, and other operators will be different.
SC.