Will HS2 come under the ownership of GBR when operational I am not sure if it would be handed over to NR after completed but will HS2 also be operated as a GBR contract too?
Avanti was/is due to operate HS2 services, so I’d say yes it does come under NR/GBR.
It's complex.
HS2 Ltd is not currently part of NR (it's a separate arm of DfT), and no policy has been stated as to what will happen when it opens.
Avanti as ICWC operator is part of the planning team for HS2 services, and is supposed to run trains on the line when it opens, many of which will run onto NR metals at the northern end of their journey.
The line will be ETCS-signalled, but where from has not been stated - it could be anywhere, and might be co-located at an NR ROC somewhere.
The precedent of HS1 is relevant.
HS1 is owned by L&CR for DfT (or possibly the Treasury), but operated and maintained by NR under contract (signalled from Ashford SCC).
But traffic rights were sold to the private sector (Canadian pension funds), and they lease the capacity to operators (Eurostar and Southeastern, and freight TOCs).
SE services are I think regulated by DfT/ORR as part of its franchise.
Eurostar is not regulated, or at least not in the same way, as it is an international service.
So I would guess HS2 will follow the same pattern.
HMG has been reluctant to put NR in charge of new lines - EWR is also under a different regime, at least for now.
HMG were also touting the sale/funding of HS2 by external capital, possibly from China - but that's gone very quiet.
Maybe all this will change now we have GBR.
Logically, you'd think HS2 Ltd would complete construction and move on to the next phase, while the operational side merges with GBR.
But I don't know where this leaves rolling stock, electrification and signalling procurement, as they are vital to the future operation of the line.