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Understanding how active galactic nuclei (AGNs) evolve through cosmic time allows us to probe the physical processes that control their evolution. We use an updated model for the evolution of masses and spins of supermassive black holes (SMBHs), coupled to the latest version of the semi-analytical model of galaxy formation GALFORM, using the Planck cosmology and a high-resolutionMillennium style dark matter simulation to make predictions for AGN and SMBH properties for 0 <z <6. We compare the model to the observed black hole mass function and the SMBH versus galaxy bulge mass relation at z = 0, and compare the predicted bolometric, hard X-ray, soft X-ray, and optical AGN luminosity functions to observations at z <6, and find that the model is in good agreement with the observations. The model predicts that at z <2 and L-bol <10(43) erg s(-1), the AGN luminosity function is dominated by objects accreting in an advection-dominated accretion flow disc state, while at higher redshifts and higher luminosities the dominant contribution is from objects accreting via a thin disc or at super-Eddington rates. The model also predicts that the AGN luminosity function at z <3 and L-bol <10(44) erg s(-1) is dominated by the contribution from AGNs fuelled by quiescent hot halo accretion, while at higher luminosities and higher redshifts, the AGN luminosity function is dominated by the contribution from AGNs fuelled by starbursts triggered by disc instabilities. We employ this model to predict the evolution of SMBH masses, Eddington ratios, and spins, finding that the median SMBH spin evolves very little for 0 <z <6.
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