We study the evolution of global shapes of galaxies using cosmological simulations. The shapes refer to the components of dark matter (DM), stars and gas at the stellar half-mass radius. Most galaxies undergo a characteristic compaction event into a blue nugget at z ∼ 2 − 4, which marks the transition from a DM-dominated central body to a self-gravitating baryonic core. We find that in the high-z, DM-dominated phase, the stellar and DM systems tend to be triaxial, preferentially prolate and mutually aligned. The elongation is supported by an anisotropic velocity dispersion that originates from the assembly of the galaxy along a dominant large-scale filament. We estimate that torques by the dominant halo are capable of inducing the elongation of the stellar system and its alignment with the halo. Then, in association with the transition to self-gravity, small-pericenter orbits puff up and the DM and stellar systems evolve into a more spherical and oblate configuration, aligned with the gas disc and associated with rotation. This transition typically occurs when the stellar mass is ∼ 10 9 M and the escape velocity in the core is ∼ 100 km s −1 , indicating that supernova feedback may be effective in keeping the core DM-dominated and the system prolate. The early elongated phase itself may be responsible for the compaction event, and the transition to the oblate phase may be associated with the subsequent quenching in the core.

We show how the existence of a relation between the star formation rate (SFR) and the gas density, i.e. the Kennicutt–Schmidt law, implies a continuous accretion of fresh gas from the environment into the discs of spiral galaxies. We present a method to derive the gas infall rate in a galaxy disc as a function of time and radius, and we apply it to the disc of the Milky Way and 21 galaxies from the THINGS sample. For the Milky Way, we found that the ratio between the past and current star formation rates is about 2–3, averaged over the disc, but it varies substantially with radius. In the other disc galaxies, there is a clear dependence of this ratio on galaxy stellar mass and Hubble type, with more constant star formation histories for small galaxies of later type. The gas accretion rate follows very closely the SFR for every galaxy and it dominates the evolution of these systems. The Milky Way has formed two‐thirds of its stars after z = 1, whilst the mass of cold gas in the disc has remained fairly constant with time. In general, all discs have accreted a significant fraction of their gas after z = 1. Accretion moves from the inner regions of the disc to the outer parts, and as a consequence star formation moves inside out as well. At z = 0, the peak of gas accretion in the Galaxy is at about 6–7 kpc from the centre.

We introduce a sub-grid model for the non-equilibrium abundance of molecular hydrogen in cosmological simulations of galaxy formation. We improve upon previous work by accounting for the unresolved structure of molecular clouds in a phenomenological way which combines both observational and numerical results on the properties of the turbulent interstellar medium. We apply the model to a cosmological simulation of the formation of a Milky Way-sized galaxy at z = 2, and compare the results to those obtained using other popular prescriptions that compute the equilibrium abundance of H 2 . In these runs we introduce an explicit link between star formation and the local H 2 abundance, and perform an additional simulation in which star formation is linked directly to the density of cold gas. In better agreement with observations, we find that the simulated galaxy produces less stars and harbours a larger gas reservoir when star formation is regulated by molecular hydrogen. In this case, the galaxy is composed of a younger stellar population as early star formation is inhibited in small, metal poor dark-matter haloes which cannot efficiently produce H 2 . The number of luminous satellites orbiting within the virial radius of the galaxy at z = 2 is reduced by 10-30 per cent in models with H 2 -regulated star formation.