A control system controlling the blood flow rate in a blood supply system (1) in which a pump (18) transports blood from a reservoir (10) toward multiple outlets (30, 26, 26a) of which one or more outlets are openable to permit flow and closable to block flow, wherein the control system comprises a monitoring arrangement (22, 32, 32a) to determine the flow rate through a first outlet (30), and a controller responsive to the monitoring arrangement and controlling the pump (18) to maintain the flow rate through the first outlet (30) at a pre-determined level. This allows a flow rate through the first outlet to be maintained independently of any active blood diversions.