  We study the accretion along streams from the cosmic web into high-redshift
massive galaxies using three sets of AMR hydro-cosmological simulations. We
find that the streams keep a roughly constant accretion rate as they penetrate
into the halo centre. The mean accretion rate follows the mass and redshift
dependence predicted for haloes by the EPS approximation, dM / dt is
proportional to Mvir^{1.25} (1 + z)^{2.5}. The distribution of the accretion
rates can well be described by a sum of two Gaussians, the primary
corresponding to "smooth inflow" and the secondary to "mergers". The same
functional form was already found for the distributions of specific star
formation rates in observations. The mass fraction in the smooth component is
60 - 90 %, insensitive to redshift or halo mass. The simulations with strong
feedback show clear signs of reaccretion due to recycling of galactic winds.
The mean accretion rate for the mergers is a factor 2 - 3 larger than that of
the smooth component. The standard deviation of the accretion rate is 0.2 - 0.3
dex, showing no trend with mass or redshift. For the smooth component it is
0.12 - 0.24 dex.
