Depends what you mean ultimately by control. At the moment the airline has two of their own employees on the Flight Deck of said asset and they in turn have the option of accepting any revised clearances ATC care to issue..or not ( even if the mighty data link is used by ATC to pass a reroute up to the FMC the "execute" button still needs a press..ooooh, the power!!!!!). Given ATC's peformance in some parts of the world I rather suspect the airlines would be very reluctant to lose that power of veto.
I was careful not to use the word
ultimate control ;-). Point very much taken on quality of ATC - but that's a reality of today, rather than something to necessarily rule out a hypothetical future.
Of course there is at least one large major economy with a single Aviation Authority controlling things, an extensive domestic aviation system, and a particularly rapacious devotion to capitalism and cost cutting: it's not beyond the bounds of reason to suspect full automation would apply to only domestic services in the first instance, say.
Relies on 100% comms reliability and if you move away from "flight following", with the "pilot" in company HQ simply available in case of a hopefully rare emergency and into the realms of having the "pilot" in company HQ monitoring every clearance I suspect it would simply be cheaper to put the pilot back on the aircraft.
My understanding of the BAE tests recently being conducted was that the aircraft would largely fly itself in all but the most extreme of emergency situations, rather than each plane having a pilot on the ground dedicated to it as per current drone operations.
If that is indeed the case, I would not expect a 1-to-1 mapping of pilots to planes; I would expect many more planes than pilots on the ground. The number of pilots required would depend on the density of aircraft in any particular sector of airspace and the probability of incidents requiring their involvement (which is another good reason why the pilot resources may be more cost effectively allocated to ATC regions rather than airlines.)