We study the accretion along streams from the cosmic web into high-redshift massive galaxies using three sets of AMR hydrocosmological 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, M˙∝Mvir1.25(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 per cent, 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 merger 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 de
