Control, Co-ordination, Tasking, Allocation..... All good words which I fear are sometimes used in the wrong context.
In my now civvy world I believe that my organisation operationally controls the use of the aircraft, our operations rooms co-ordinate SAR operations (Civil maritime in the main) and task the SAR units involved and, under an agreement with the RAF we contact ARCCK who allocate the aircraft to be used just in case there is another aircraft in the area of which we are unaware.
If the job is within 30 miles of the base we can go ahead and task, launch, allocate that helicopter without recourse to ARCCK. Of course the ARCCK would be contacted ASAP and informed of the situation to enable them to update their big picture and ensure that the future allocation process is not affected should another job arise.
As a SAR Co-ordinator it would be churlish, possibly grossly negligent of me not to prioritise should a request arise from any other organisation for a helo (or any other unit for that matter) already involved in an operation we are co-ordinating.
Regarding Search Planning, we have a number of tools in the box (and some out of the box) which can be used to determine a search area. I can assure you that the subsequeent board of enquiry does not even figure when determining a search area and/or allocating SAR resources.
Regarding termination of search, something which I have been involved in on a number of occasions and it's a task not undertaken or a decision made lightly, certainly not by one unit on-scene. The decision should be, and is, made in consultation with many of the parties involved be they on-scene, in Ops Rooms or Duty Officers at a number of levels.
We may also be approached by other organisations for the use of our aircraft and given that it's not involved in its' primary role then every effort will generally be made to provide it.
I see multi-organisation operations increasing monthly and in the main they work very well. Lets hope that what progress there is continues and that we can all live happily ever after.
Be safe and best regards to all.