  (abridged) The physics of diffuse gas accretion and the properties of the
cold and hot modes of accretion onto proto-galaxies between z=2 and z=5.4 is
investigated using the large cosmological simulation performed with the RAMSES
code on the MareNostrum supercomputing facility. Galactic winds, chemical
enrichment, UV background heating and radiative cooling are taken into account
in this very high resolution simulation. Using accretion--weighted temperature
histograms, we have perfomed two different measurements of the thermal state of
the gas accreted towards the central galaxy. The first measurement, performed
using accretion--weighted histograms on a spherical surface of radius 0.2 Rvir
centred on the densest gas structure near the halo centre of mass, is a good
indicator of the presence of an accretion shock in the vicinity of the galactic
disc. We define the hot shock mass, Mshock, as the typical halo mass separating
cold dominated from hot dominated accretion in the vicinity of the galaxy. The
second measurement is performed by radially averaging histograms between 0.2
Rvir and Rvir, in order to detect radially extended structures such as gas
filaments: this is a good proxy for detecting cold streams feeding the central
galaxy. We define Mstream as the transition mass separating cold dominated from
hot dominated accretion in the outer halo, marking the disappearance of these
cold streams. We find a hot shock transition mass of Mshock=10^{11.6} Msun
(dark matter), with no significant evolution with redshift. Conversely, we find
that Mstream increases sharply with z. Our measurements are in agreement with
the analytical predictions of Birnboim & Dekel (2003) and Dekel & Birnboim
(2006), if we correct their model by assuming low metallicity (< 10^{-3} Zsun)
for the filaments, correspondingly to our measurements.

Astrophysics