A reproduction system for producing and collating copies from a set of document sheets comprises a copy set collecting and storage arrangement for a high speed copy reproduction system or duplicator machine (11) having a finishing station (130). The arrangement includes an elevator (138) for collecting finished copy sets in a stack and a conveyor (140) for receiving one or more stacks from the elevator. Controls are devised for "limitless" finishing wherein the duplicator is placed in Standby, count holding condition when the full storage capacity has been reached and the programmed reproduction run has not been achieved. The controls will effect automatic start-up again when one or more of the stacks have been removed until once again the capacity has been reached and the reproduction run has not been completed.