Muldrake,
just to clarify eyeinthesky.
the area (terminal) guys get the A/C into the stack, starting at the lowest level and laddering up. Once in the stack, or approaching the stack going to the correct level, they are transferred to Director who takes over and takes the A/C out when it is time to do so. The area guys then feed A/C into the lowest available level at any given time, and so it continues.
As HD stated, in bad weather, it can be a bit of a grey area, with lots of coordination and a blurring of responsibilities, such as yesterday and Tuesday.