  We examine the far-IR properties of a sample of 5391 optically selected QSOs
in the 0.5<z<2.65 redshift range down to log[nuLnu,2500 (erg/s)]>44.7, using
SPIRE data from Herschel-ATLAS. We split the sample in a grid of 74
luminosity-redshift bins and compute the average optical-infrared spectral
energy distribution (SED) in each bin. By normalising an intrinsic AGN template
to the AGN optical power (at 5100A) we decompose the total infrared emission
(L_IR; 8-1000um) into an AGN (L_IR,AGN) and star-forming component (L_IR,SF).
We find that the AGN contribution to L_IR increases as a function of AGN power
which manifests as a reduction of the `far-IR bump' in the average QSO SEDs. We
note that L_IR,SF does not correlate with AGN power; the mean star formation
rates (SFRs) of AGN host galaxies are a function of redshift only and they
range from ~6 Msun/yr at z~0 to a plateau of <200 Msun/yr at z~2.6. Our results
indicate that the accuracy of far-IR emission as a proxy for SFR decreases with
increasing AGN luminosity. We show that, at any given redshift, observed trends
between infrared luminosity (whether monochromatic or total) and AGN power (in
the optical or X-rays) can be explained by a simple model which is the sum of
two components: (A) the infrared emission from star-formation, uncorrelated
with AGN power and (B) the infrared emission from AGN, directly proportional to
AGN power in the optical or X-rays.
