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.

27 pages, 8 figures, 2 tables. Accepted for publication in ApJ