Alessandro Lupi - November 17, 2017 The natural emergence of the SFR-H2 surface density relation in galaxy simulations Recent developments of numerical techniques and sub-grid modelling have allowed to investigate in more detail the galaxy properties and the effect of star formation (SF), and stellar and AGN feedback, on the host evolution. In particular, several groups have started to employ H2-based SF prescriptions in numerical simulations, motivated by the observational evidence of a linear correlation between the star formation (SF) rate and the molecular hydrogen (H2) surface densities in nearby star-forming galaxies. However, recent theoretical studies have revealed a lack of causal connection between H2 and SF, suggesting that the formation of H2 could be controlled by SF and not vice versa. I will present a new sub-grid model, implemented in the meshless code GIZMO, to follow the formation and dissociation of H2, via the chemistry package KROME, including gas and dust shielding, self-shielding of molecular gas, SF, supernova feedback, and extragalactic and local stellar radiation (modelled both as a sub-grid model and with on-the-fly radiative transfer calculations). I will discuss the results of a suite of simulations of an isolated gas-rich galaxy at z=3, showing how it can naturally reproduce at the same time the Schmidt-Kennicutt law for total gas (HI+H2) the SF-H2 correlation, without any a priori dependence of SF on the H2 abundance. I will finally present, as a possible application of the model, a study of the the kinematics and dynamics of molecular gas in high-redshift quasars.