From my pattern number list (made mostly from my observations over many years) the 581 cover was made for the No. 0, 00, and 000 Service (of Serving?) kettle plus the 109 p/n table service dutch oven (not a toy but just a small, individual serving sized pot as were the Service Kettles. I belive the Al Carder pot was one of Griswold existing pots (or slightly modified for Carder-who is he anyway??) as was the 581 Carder cover. Sometimes Griswold would use the same pattern number for slightly different pieces made at different times.
Steve