If and when HS2 is up and running, to Birmingham at least, the question will be who runs the services along the line.
If present government policy is to be followed the logical operator would be the dominant one at the London terminus. Since the terminus will be Euston then this is Virgin Trains (at the moment). Thus it can be foreseen that the operator from Euston will be Virgin Trains.
However, Virgin Trains operates the inter-city services from Euston to Northwest England and Glasgow so can be expected to benefit hugely, as compared to its competitors, from continuing to run those services using the HS2 for that part of the service south of Birmingham.
This might prove too much for the government which might well likely prefer more direct competition. In that case as Chiltern would be a loser on its services to Birmingham from Marylebone. There would be a strong case for Chiltern(which is DB) to run the trains to Birmingham only.
If stage 2 of the plans for HS2 are accepted then one could well see East Coast running services up HS2 to York and onwards to Newcastle and Edinburgh. The services to Leeds(only) would then be run by East Midlands Trains.
Add in Grand Central to Sunderland and even possibly Scot Rail services then we would end up with a real pot-pourri.Thus we would have lots of different companies operating semi-competitively. Is it too much to imagine?