Left and central panels: starburstiness R_SB as a function of M_∗ in three redshift bins. The filled contours in the left panels correspond to the predicted average values of the AGN X-ray luminosity for bins of different M_∗ and R_SB. The luminosity values are equally spaced in logarithmic scale from L_X = 10^42.5 erg/s for the lightest filled region to L_X = 10⁴⁵ erg/s for the darkest. The filled (dotted) contours in the central panel correspond to equally spaced values of the density (per Mpc³) of model AGNs with L_X ≥ 10⁴⁴ erg/s (L_X ≥ 10^43.8 erg/s) in logarithmic scale: from 10^-9 for the lightest filled region to 10^-6 for the darkest. The data points indicate the XMM-COSMOS AGNs with L_X ≥ 10⁴⁴ erg/s. Circles and arrows indicate AGNs with SFR derived from L_FIR, while triangles indicate AGNs with SFR derived from SED fitting. Circles and triangles are color coded according to their X-ray luminosity in the left panels. Solid lines show the position of the galaxy main sequence, while dashed lines denote the limits of the starburst and passive areas, defined as R_SB > 4 and R_SB < 1/4, respectively. Vertical dashed lines indicate the stellar mass limits adopted in deriving the fraction of AGN hosted in starburst galaxies in Sect. 4.2. Right panels: starburstiness distribution of model AGNs. The solid histograms refer to galaxies dominated by the quiescent mode of star formation (SFR_q > SFR_b), while the dotted histograms refer to galaxies dominated by the burst component of star formation (SFRb > SFR_q). Solid and dashed lines as in the left panels.