Upper panel: predicted distribution of galaxies in the M_BH−M_K,disc plane from our SAM (contour plot), where M_K,disc is the K-band magnitude of the stellar disc. The data are from Kormendy & Ho (2013): black diamonds refer to spiral galaxies with classical bulges, while blue diamonds correspond to galaxies with a pseudo-bulge. The dashed line in the contour plot shows the linear fit log M_BH/M_⊙ = −0.264 log  (M_K,disc/M_⊙) + 1.97, while the histograms on the top show the average value and the scatter Δlog M_BH of the distribution of log M_BH/M_⊙. Lower panel: each coloured path shows the time evolution of the BH mass M_BH(t) and disc mass M_{∗ ,D}(t) contributed by all progenitors of a few selected galaxies. The circles show the onset of an active AGN phase; their size corresponds to the logarithm of the Eddington ratio λ ≡ Ṁ_BH/Ṁ_Edd as shown in the legend.