  We study a model in which supermassive black holes (SMBHs) can grow by the
combined action of gas accretion on heavy seeds and mergers of both heavy
(m_s^h=10^5 Msol) and light (m_s^l = 10^2 Msol) seeds. The former result from
the direct collapse of gas in T_s^h >1.5x10^4K, H_2-free halos; the latter are
the endproduct of a standard H_2-based star formation process. The H_2-free
condition is attained by exposing halos to a strong (J_21 > 10^3) Lyman-Werner
UV background produced by both accreting BHs and stars, thus establishing a
self-regulated growth regime. We find that this condition is met already at z
close to 18 in the highly biased regions in which quasars are born. The key
parameter allowing the formation of SMBHs by z=6-7 is the fraction of halos
that can form heavy seeds: the minimum requirement is that f_heavy>0.001; SMBH
as large as 2x10^10 Msol can be obtained when f_heavy approaches unity.
Independently of f_heavy, the model produces a high-z stellar bulge-black hole
mass relation which is steeper than the local one, implying that SMBHs formed
before their bulge was in place. The formation of heavy seeds, allowed by the
Lyman-Werner radiative feedback in the quasar-forming environment, is crucial
to achieve a fast growth of the SMBH by merger events in the early phases of
its evolution, i.e. z>7. The UV photon production is largely dominated by stars
in galaxies, i.e. black hole accretion radiation is sub-dominant.
Interestingly, we find that the final mass of light BHs and of the SMBH in the
quasar is roughly equal by z=6; by the same time only 19% of the initial baryon
content has been converted into stars. The SMBH growth is dominated at all
epochs z > 7.2 by mergers (exceeding accretion by a factor 2-50); at later
times accretion becomes by far the most important growth channel. We finally
discuss possible shortcomings of the model.
