Eventually the parents die, leaving the children to run the world.
Yup.. and there's really no need for skynet to KILL all humans.. I think humans would naturally relinquish, and trade up to neural net upload.
How many humans left alive would depend on why the machines want to keep humans alive.
Pets? Unlikely.
Food? Nope.
Energy, like in Matrix? Possibly.
They'd probably use algae for a solar bio battery.. by burning lipids rather than humans..
as to WHY keep humans around.. the Machine is as human as any human.. it's the next step.. we really should remove this boundary in description of our creations as external to ourselves..
A sufficiently complex machine is as much a human, as human children, and it is by the same labor that they are created, and with the same interest.. Our continuation..