  We discuss a model for the early assembly of supermassive black holes (SMBHs)
at the center of galaxies that trace their hierarchical build-up far up in the
dark halo `merger tree'. Motivated by the observations of luminous quasars
around redshift z=6 with SMBH masses of billion solar masses, we assess the
possibility of an early phase of stable super-critical quasi-spherical
accretion in the BHs hosted by metal free halos with virial temperature larger
than 10000 K. We assume that the first `seed' black holes formed with
intermediate masses following the collapse of the first generation of stars, in
mini-halos collapsing at z=20-30 from high peaks of density fluctuations. In
high redshift halos with virial temperature larger than 10000 K, conditions
exist for the formation of a fat disc of gas at T_gas=5000-10000 K. Cooling via
hydrogen atomic lines is in fact effective in these comparatively massive
halos. The cooling and collapse of an initially spherical configuration of gas
leads to a rotationally supported disc at the center of the halo if baryons
preserve their specific angular momentum during collapse. The conditions for
the formation of the gas disc and accretion onto a central black holes out of
this supply of gas are investigated, as well as the feedback of the emission
onto the host and onto the intergalactic medium. We find that even a short
phase of supercritical accretion eases the requirements set by the z=6 quasars.
