Sorting systems and methods for large quantities of items in industrial processes are described. The systems, devices and methods are for receiving, sorting and removing items dynamically. A first group of items, such as letters or other mail pieces, are injected by a belt into a pocket to a form a first stack, and a progressive displacement divider with amplified output for a given input is extended near the first stack. The divider allows for a second group of items to either be injected to form a second stack behind the divider, or to be diverted and injected into another pocket. The first stack can be removed while the second group is being injected.