The ORR consider the railways to effectively be nationalised for accounting purposes at the moment
But I suspect that isn't the point of your thread!
Would all the stock be retained for the same routes or would they be shared (for example, would Pendolinos work on the ECML?)?
I think the example you give is very unlikely given it doesn't really make any sense to do that (ie. there aren't any big advantages and lots of expensive disadvantages).
More broadly, perhaps. It might mean that some of the smaller subfleets ended up being amalgamated (eg. 158s, 170s), but that's currently possible now anyway so...
Would we go back to the old InterCity, Network SouthEast and Regional Railways arms of British Rail, or would they be called something else?
I would say very unlikely. You might end up with something like Network Rail (as has been suggested) or something SRA-like in charge of the nationwide strategy, but I would say individual, autonomous and sensibly divided franchises have worked quite well logistically and operationally (looking at the big picture over 25 years).
A concession model is perhaps more likely, where private operators are contracted to run services with the government taking the revenue risk. That would be similar to TfL Rail/Overground services, but whether that would work at a national scale is up for debate.
You might also end up with more LNER-style operations, where it's a private company but wholly owned by the DfT. That seems to work quite well as the private company has an incentive to make a profit, only has one shareholder and retains a lot of operational autonomy and flexibility. The last thing you want is the DfT micromanaging...
What would the liveries look like?
Similar.
DfT has required agnostic branding/liveries in all the recent franchises (hence Great Northern, Thameslink, LNER, Greater Anglia). AWC is the exception, rather than the rule.
