Do the central black holes in galaxies represent the remnants from single first generation stars?

This seems unlikely, but when talking about the early universe, nothing can be ruled out completely.

The most plausible picture has these behemoths starting out as perhaps a cluster of very massive first generation stars each a few hundred times the mass of the Sun. After they went supernova in a few million years after their birth, they produced clusters of black holes which quickly merged into thousand solar mass black holes like the ones we now find in the cores of some globular clusters.

Then a feeding frenzy began as frequent host galaxy collisions continued to dump stars and matter into trajectories that intersected the feeding black holes. At a few solar masses per year, like what you easily get for quasars, you end up with billion solar mass black holes after a few billion years. Also, primordial matter fluctuations left over from the Big Bang might also have started the universe out with massive black holes which became the seeds for galaxies that accreted around them over time. We do not know which of these is the actual situation. They might BOTH be true to some degree!