  There is growing observational evidence for a population of supermassive
black holes (SMBHs) in galactic bulges. We examine in detail the conditions
under which these black holes must have originated from primordial black holes
(PBHs). We consider the merging and accretion history experienced by SMBHs to
find that, whereas it is possible that they were formed by purely astrophysical
processes, this is unlikely and most probably a populations of primordial
progenitors is necessary. We identify the mass distribution and comoving
density of this population and then propose a cosmological scenario producing
PBHs with the right properties. Although this is not essential we consider PBHs
produced at the end of a period of inflation with a blue spectrum of
fluctuations. We constrain the value of the spectral tilt in order to obtain
the required PBH comoving density. We then assume that PBHs grow by accreting
quintessence showing that their mass scales like the horizon mass while the
quintessence field itself is scaling. We find that if scaling is broken just
before nucleosynthesis (as is the case with some attractive non-minimally
coupled models) we obtain the appropriate PBH mass distribution. Hawking
evaporation is negligible in most cases, but we also discuss situations in
which the interplay of accretion and evaporation is relevant.
