Lumber does not have this quite correct.
HELAIRDETS are given OPCOM to the Ship, when they embark. There are residual authorities which are retained by the RCAF (things like flight safety, airworthiness, maintenance policy). When the ship chops to CJOC, the
JFACC (double-hatted as Comd 1 Cdn Air Div) exercises a command function over the HELAIRDET (which becomes known as an Air Task Force, in RCAF parlance).
Because the institutional RCAF knowledge of Naval Doctrine and the realities of life onboard an RCN ship is poor (at best), it leads to a lot of uncomfortable moments for the HELAIRDET Commander when the CAOC in Winnipeg begins to ping him/her directly to either gather information (daily quad slide :
) or to issue direction that would impact the Ship's movement without first consulting the CO of the ship, or (a more recent tendency) attempt to place the HELAIRDET under the nearest RCAF Air Task Force and then task them on the daily ATO- despite the fact that naval helicopters are an organic asset and tasked by every other navy in the world in a completely differ the fashion.
It is a buggers mess as the RCAF tries to fit the HELAIRDET concept into its USAF centric C2 structure, to put it mildly...