Mass and spin of massive black holes (BHs) at the centre of galaxies evolve due to gas accretion and mergers with other BHs. Besides affecting e.g. the evolution of relativistic jets, the BH spin determines the efficiency with which the BH radiates energy. Using cosmological, hydrodynamical simulations, we investigate the evolution of the BH spin across cosmic time and its role in controlling the joint growth of supermassive BHs and their host galaxies. We implement a sub-resolution prescription that models the BH spin, accounting for both BH coalescence and misaligned accretion through a geometrically thin, optically thick disc. We investigate how BH spin evolves in two idealised setups, in zoomed-in simulations, and in a cosmological volume. The latter simulation allows us to retrieve statistically robust results as for the evolution and distribution of BH spins as a function of BH properties. We find that BHs with MBH≲2×107M⊙ grow through gas accretion, occurring mostly in a coherent fashion that favours spin-up. Above MBH≳2×107 M⊙ the gas angular momentum directions of subsequent accretion episodes are often uncorrelated with each other. The probability of counter-rotating accretion and hence spin-down increases with BH mass. In the latter mass regime, BH coalescence plays an important role. The spin magnitude displays a wide variety of histories, depending on the dynamical state of the gas feeding the BH and the relative contribution of mergers and gas accretion. As a result of their combined effect, we observe a broad range of values of the spin magnitude at the high-mass end. Our predictions for the distributions of BH spin and spin-dependent radiative efficiency as a function of BH mass are in very good agreement with observations.
