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We investigate the mean star formation rates (SFRs) in the host galaxies of ~3000 optically selected QSOs from the SDSS survey within the Herschel-ATLAS fields, and a radio-luminous sub-sample, covering the redshift range of z = 0.2-2.5. Using WISE & Herschel photometry (12 - 500��m) we construct composite SEDs in bins of redshift and AGN luminosity. We perform SED fitting to measure the mean infrared luminosity due to star formation, removing the contamination from AGN emission. We find that the mean SFRs show a weak positive trend with increasing AGN luminosity. However, we demonstrate that the observed trend could be due to an increase in black hole (BH) mass (and a consequent increase of inferred stellar mass) with increasing AGN luminosity. We compare to a sample of X-ray selected AGN and find that the two populations have consistent mean SFRs when matched in AGN luminosity and redshift. On the basis of the available virial BH masses, and the evolving BH mass to stellar mass relationship, we find that the mean SFRs of our QSO sample are consistent with those of main sequence star-forming galaxies. Similarly, the radio-luminous QSOs have mean SFRs that are consistent with both the overall QSO sample and with star-forming galaxies on the main sequence. In conclusion, on average QSOs reside on the main sequence of star-forming galaxies, and the observed positive trend between the mean SFRs and AGN luminosity can be attributed to BH mass and redshift dependencies., 22 pages (incl. appendix), 17 Figures, re-submitted to MNRAS with referee comments addressed

et al., We analyse the stellar populations in the host galaxies of 53 X-ray selected optically dull active galactic nuclei (AGN) at 0.34 < z < 1.07 with ultradeep (mAB = 26.5, 3σ) optical mediumband (R ~ 50) photometry from the Survey for High-z Absorption Red and Dead Sources (SHARDS). The spectral resolution of SHARDS allows us to consistently measure the strength of the 4000Å break, Dn(4000), a reliable age indicator for stellar populations.We confirm that most X-ray selected moderate-luminosity AGN (LX < 1044 erg s-1) are hosted by massive galaxies (typically M*>1010.5 M⊙) and that the observed fraction of galaxies hosting an AGN increases with the stellar mass. A careful selection of random control samples of inactive galaxies allows us to remove the stellar mass and redshift dependences of the AGN fraction to explore trends with several stellar age indicators. We find no significant differences in the distribution of the rest-frame U - V colour for AGN hosts and inactive galaxies, in agreement with previous results. However, we find significantly shallower 4000Å breaks in AGN hosts, indicative of younger stellar populations.With the help of a model-independent determination of the extinction, we obtain extinction-corrected U - V colours and light-weighted average stellar ages. We find that AGN hosts have younger stellar populations and higher extinction compared to inactive galaxies with the same stellar mass and at the same redshift. We find a highly significant excess of AGN hosts with Dn(4000) ~ 1.4 and light-weighted average stellar ages of 300-500 Myr, as well as a deficit of AGN in intrinsic red galaxies. We interpret failure in recognizing these trends in previous studies as a consequence of the balancing effect in observed colours of the age-extinction degeneracy. © 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society., AH-C and AA-H acknowledge funding by the Universidad de Cantabria Augusto González Linares programme and the Spanish Plan Nacional de Astronomía y Astrofísica under grant AYA2012-31447. PE and PGP-G acknowledge support from the Spanish Plan Nacional grant AYA2012-31277.