What supplements to the flight manual (FM) should be taken on board, and who is responsible for keeping them up to date

In accordance with current regulations, it is the responsibility of the owner/operator that the flight manual is updated. 
The FM and its supplements should reflect the configuration of the aircraft at the time of inspection, and only applicable supplements should be carried on board. If it is decided to carry all supplements on board, it must be possible to demonstrate which supplements are applicable to the current configuration.