  We investigate the physical conditions for the growth of intermediate mass
seed black holes assumed to have formed from remnants of the first generation
of massive stars. We follow the collapse of high-sigma halos with Tvir > 1e4 K
using cosmological, smooth-particle hydrodynamic (SPH) simulations in the
standard LCDM model. During collapse of the parent halo the seed holes are
incorporated through mergers into larger systems and accrete mass from the
surrounding gas. We include a self-consistent treatment of star formation,
black hole accretion and associated feedback processes. Even under optimistic
assumptions for the seed black hole mass and for efficient merger rates, we
find that seed holes in halos M<1e10 Msun never reach the conditions for
critical Eddington growth. Most of the black hole growth in this regime is
determined by the initial mass and the merger rates. Critical accretion rates
are reached, albeit only after a significant delay, at the time of collapse
z~7) for 3-4 sigma halos of M~1e11 Msun. Our results imply M_BH = 5e6 Msun
(M_halo/1e11 Msun)^0.78 at the time of collapse. The required conditions of
Eddington growth to explain the build-up of supermassive black holes (~1e9
Msun), as implied by Sloan quasars at z>6, are therefore hard to meet in such a
scenario. Without a 'jump-start' these conditions may be only achieved in
extremely rare halos with M_halo > 1e13 Msun that collapsed before z~6. The
sub-Eddington regime in which black holes holes accrete at early time implies a
small contribution to the reionization by miniquasar but still sufficient to
cause appreciable heating of the IGM at z<15-18.
