Context. Feedback from accreting supermassive black holes is often identified as the main mechanism responsible for regulating star-formation in AGN host galaxies. However, the relationships between AGN activity, radiation, winds, and star-formation are complex and still far from being understood. Aims. We study scaling relations between AGN properties, host galaxy properties and AGN winds. We then evaluate the wind mean impact on the global star-formation history, taking into account the short AGN duty cycle with respect to that of star-formation. Methods. We first collect AGN wind observations for 94 AGN with detected massive winds at sub-pc to kpc spatial scales. We then fold AGN wind scaling relations with AGN luminosity functions, to evaluate the average AGN wind mass-loading factor as a function of cosmic time. Results. We find strong correlations between the AGN molecular and ionised wind mass outflow rates and the AGN bolometric luminosity. The power law scaling is steeper for ionised winds (slope 1.29±0.38) than for molecular winds (0.76±0.06), meaning that the two rates converge at high bolometric luminosities. The molecular gas depletion timescale and the molecular gas fraction of galaxies hosting powerful AGN driven winds are 3-10 times shorter and smaller than those of main-sequence galaxies with similar star-formation rate, stellar mass and redshift. These findings suggest that, at high AGN bolometric luminosity, the reduced molecular gas fraction may be due to the destruction of molecules by the wind, leading to a larger fraction of gas in the atomic ionised phase. The AGN wind mass-loading factor η =ṀOF /SFR is systematically higher than that of starburst driven winds. Conclusions. Our analysis shows that AGN winds are, on average, powerful enough to clean galaxies from their molecular gas only in massive systems at z < ∼ 2, i.e. a strong form of co-evolution between SMBHs and galaxies appears to break down for the least massive galaxies.

Context. The AGN bolometric correction is a key element to understand BH demographics and compute accurate BH accretion histories from AGN luminosities. However, current estimates still differ from each other by up to a factor of two to three, and rely on extrapolations at the lowest and highest luminosities. Aims. Here we revisit this fundamental issue presenting general hard X-ray (K X ) and optical (K O ) bolometric corrections, computed combining several AGN samples spanning the widest (about 7 dex) luminosity range ever used for this kind of studies. Methods. We analysed a total of ∼ 1000 type 1 and type 2 AGN for which a dedicated SED-fitting has been carried out. Results. We provide a bolometric correction separately for type 1 and type 2 AGN; the two bolometric corrections results to be in agreement in the overlapping luminosity range and therefore, for the first time, a universal bolometric correction for the whole AGN sample (both type 1 and type 2) has been computed. We found that K X is fairly constant at log(L BOL /L ⊙ ) < 11, while it increases up to about one order of magnitude at log(L BOL /L ⊙ ) ∼ 14.5. A similar increasing trend has been observed when its dependence on either the Eddington ratio or the BH mass is considered, while no dependence on redshift up to z ∼ 3.5 has been found. On the contrary, the optical bolometric correction appears to be fairly constant (i.e. K O ∼ 5) whatever is the independent variable. We also verified that our bolometric corrections correctly predict the AGN bolometric luminosity functions. According to this analysis, our bolometric corrections can be applied to the whole AGN population in a wide range of luminosity and redshift.