From my understanding, Atlas Air perfroms all maintinence for the aircraft that BA World Cargo uses. Under the ACMI contract, Atlas Air pays for and operates the aircraft, pays the crew, performs and pays for the maintenance and insurance for the aircraft. British Airways pays for all user fees. These can include airport fees, fuel costs and cargo insurance. As long as BA is paying to "rent" the plane under the ACMI contract, they will get it back after it gets checked out, or another Atlas Air 747-400F will go in its place.
Regards from St Louis!