First three panels: cumulative distributions of SFE for the samples of star-forming galaxies (green line), unobscured (blue), and dusty (red) QSOs in the three redshift intervals specified along the upper edge of the figures. All targets collected from the literature (for which SFE measurements can be derived) are used to construct the cumulative distributions; in the first panel, we do not report the cumulative distribution of unobscured AGN (our sample only includes two of these objects at 1≤ z ≤ 2). The figures show the clear separation in SFE between AGN and SFGs. Right panel: cumulative distribution of SFE for the same three samples, considering the entire redshift range covered by our targets. Short-dashed red line: cumulative SFE distribution of dusty AGN obtained by reducing by 60% all their IR luminosities to test for the impact of cool, AGN-heated dust (e.g. Duras et al. 2017; see Sect. 4.1.2 for details). Long-dashed red line: distribution of dusty AGN for which a high-quality L_IR has been measured through an SED-decomposition into AGN and galaxy emission.