  We present a semi-analytical model for the formation and evolution of a high
redshift quasar (QSO). We reconstruct a set of hierarchical merger histories of
a 10^13 Msun dark matter halo and model the evolution of the corresponding
galaxy and of its central super massive black hole. The code GAMETE/QSODUST
consistently follows: the black hole assembly via both coalescence with other
black holes and gas accretion; the build up and star formation history of the
quasar host galaxy, driven by binary mergers and mass accretion; the evolution
of gas, stars, metals in the interstellar medium (ISM), accounting for mass
exchanges with the external medium (infall and outflow processes); dust
formation in Supernova (SN) ejecta and in the stellar atmosphere of Asymptotic
Giant Branch (AGB) stars, dust destruction by interstellar shocks and grain
growth in molecular clouds; the AGN feedback which powers a galactic-scale
wind, self-regulating the black hole growth and eventually halting star
formation.We use this model to study the case of SDSS J1148+5251 observed at
redshift 6.4, exploring different star formation histories for the QSO host
galaxy.
