  We present near-infrared imaging obtained with ESO VLT/ISAAC of a sample of
16 low luminosity radio-quiet quasars at the epoch around the peak of the
quasar activity (2 < z < 3), aimed at investigating their host galaxies. For 11
quasars, we are able to detect the host galaxies and derive their properties,
while for the other five quasars, upper limits to the host luminosity are
estimated. The luminosities of the host galaxies of radio-quiet quasars at high
redshift are in the range of those of massive inactive elliptical galaxies.
  This work complements our previous systematic study of quasar hosts aimed to
trace the cosmological luminosity evolution of the host galaxies up to z ~2 and
extends our pilot study of a few luminous quasars at z > 2. The luminosity
trend with cosmic epoch resembles that observed for massive inactive galaxies,
suggesting a similar star formation history. In particular, both quasar host
galaxies and massive inactive galaxies appear mostly assembled already at the
peak age of the quasar activity. This result is of key importance for testing
the models of joint formation and evolution of galaxies and their active
nuclei.
