  By using AMR cosmological hydrodynamic N-body zoom-in simulations, with the
RAMSES code, we studied the mass transport processes onto galactic nuclei from
high redshift up to $z\sim6$. Due to the large dynamical range of the
simulations we were able to study the mass accretion process on scales from
$\sim50[kpc]$ to $\sim$ few $1[pc]$. We studied the BH growth on to the
galactic center in relation with the mass transport processes associated to
both the Reynolds stress and the gravitational stress on the disc. Such
methodology allowed us to identify the main mass transport process as a
function of the scales of the problem. We found that in simulations that
include radiative cooling and SNe feedback, the SMBH grows at the Eddington
limit for some periods of time presenting $\langle f_{EDD}\rangle\approx 0.5$
throughout its evolution. The $\alpha$ parameter is dominated by the Reynolds
term, $\alpha_R$, with $\alpha_R\gg 1$. The gravitational part of the $\alpha$
parameter, $\alpha_G$, has an increasing trend toward the galactic center at
higher redshifts, with values $\alpha_G\sim 1$ at radii <$\sim$ few $ 10^1[pc]$
contributing to the BH fueling. In terms of torques, we also found that gravity
has an increasing contribution toward the galactic center at earlier epochs
with a mixed contribution above $\sim 100 [pc]$. This complementary work
between pressure gradients and gravitational potential gradients allows an
efficient mass transport on the disc with average mass accretion rates of the
order $\sim$ few $1 [M_{\odot}/yr]$. These level of SMBH accretion rates found
in our cosmological simulations are needed in all models of SMBH growth that
attempt to explain the formation of redshift $6-7$ quasars.
