Luminosity versus redshift distribution of the AGN samples used in this work. Top: intrinsic 2–10 keV rest-frame X-ray luminosity L_X vs. redshift z distribution of the full KASHz (purple pentagons) and SUPER (blue circles) surveys. SUPER ALMA targets are from C21. The side panel shows the density distribution of SUPER (blue) and KASHz (purple) targets. Bottom: bolometric luminosity L_Bol vs. redshift z distribution of the AGN targeted by ALMA and included in this work. For the KASHz (purple pentagons) and SUPER (blue circles) targets included in this panel, the bolometric luminosity was derived from SED fitting in this work (see Appendix D), in C18, and in C21. The side panel shows the density distribution of the samples. The black dots mark the six targets discarded because they were missing at least one parameter of interest for our analysis; the white dots mark the three targets that do not allow f_gas to be computed.