  A combination of ground-based (NTT and VLT) and HST (HDF-N and HDF-S) public
imaging surveys have been used to collect a sample of 1712 I-selected and 319
$K\leq 21$ galaxies. Photometric redshifts have been obtained for all these
galaxies. The results have been compared with the prediction of an analytic
rendition of the current CDM hierarchical models for galaxy formation. We focus
in particular on two observed quantities: the galaxy redshift distribution at
K<21 and the evolution of the UV luminosity density. The derived photometric
redshift distribution is in agreement with the hierarchical CDM prediction,
with a fraction of only 5% of galaxies detected at z>2. This result strongly
supports hierarchical scenarios where present-day massive galaxies are the
result of merging processes. The observed UV luminosity density in the
I-selected sample is confined within a factor of 4 over the whole range
0<z<4.5. CDM models in a critical Universe are not able to produce the density
of UV photons that is observed at z>3. CDM models in $\Lambda$-dominated
universe are in better agreement at 3<z<4.5, but predict a pronounced peak at
z~1.5 and a drop by a factor of 8 from z=1.5 to z=4 that is not observed in the
data. We conclude that improvements are required in the treatment of the
physical processes directly related to the SFR, e.g. the starbust activity in
merger processes and/or different feedback to the star formation activity.
