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In order to constrain the physical processes that regulate and downsize the active galactic nucleus (AGN) population, the predictions of the model for the rise of galaxies and active nuclei (morgana) are compared to luminosity functions (LFs) of AGNs in the optical, soft and hard X-ray bands, to the local black hole (BH)–bulge mass relation and to the observed X-ray number counts and background. We also give predictions on the accretion rate of AGNs in units of the Eddington rate and on the BH–bulge relation expected at high redshift. We find that it is possible to reproduce the downsizing of AGNs within the hierarchical Lambda cold dark matter cosmogony and that the most likely cause of this downsizing is the stellar kinetic feedback that arises in star-forming bulges as a consequence of the high level of turbulence and leads to a massive removal of cold gas in small elliptical galaxies. At the same time, to obtain good fits to the number of bright quasars we require that quasar-triggered galactic winds self-limit the accretion on to BHs; however, the very high degree of complexity of the physics of these winds, coupled with our poor understanding of it, hampers more robust conclusions. In all cases, the predicted BH–bulge relation steepens considerably with respect to the observed one at bulge masses ; this problem is related to a known excess in the predicted number of small bulges, common to most similar models, so that the reproduction of the correct number of faint AGNs is done at the cost of underestimating their BH masses. This highlights an insufficient downsizing of elliptical galaxies, and hints at another feedback mechanism able to act on the compact discs that form and soon merge at high redshift. The results of this paper reinforce the need for direct investigations of the feedback mechanisms in active galaxies that will be possible with the next generation of astronomical telescopes from submm to X-rays. [ABSTRACT FROM AUTHOR]