Note to self, "Remember to use the words 'Onageristic Estimate' in next piece of staff work!"
JFAC HQ done above.
JFACC Joint Force Air Component Commander (Usually Gp Capt or above). Think of the JFACC as a kind of mobile Combined Air Ops Centre (CAOC). The UK JFAC HQ is a relatively small core organization which relies on external reinforcement (ERS) when they deploy. They also rely largely on host-nation support or specialist deployable UK assistance (eg TCW) for comms and IT support.
As with the CAOC, they issue the ATO and ACO if they have OPCOM of assigned forces and an Area of Responsibility (AOR).
As Shawshank suggests, though, Google is pretty good for explaining.
STH