Wiggy is mostly right about BA although all loadsheets are done by ACARS now unless it’s unserviceable.
Preliminary loadsheet arrives at -40 (-30 on shorthaul). Performance is calculated based off these figures with a safety margin factored in. During the taxi out, a final loadsheet is produced which is a simplified version of the preliminary. This states whether it’s within certain tolerances of the preliminary or not. If it’s ‘compliant’, you can depart and update the ZFW and CG at a point of low workload usually in the climb. If it’s not compliant, then you may need to re-run the takeoff performance and/or reset the trim.
Signatures are now electronic too - the acknowledge prompt on ACARS acts as the signature. Also, LMCs aren’t allowed anymore. The final loadsheet should reflect the conditions of the aircraft (pax, freight, fuel etc).