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(Abridged) We study relationships between the SFR and the nuclear propertiesof X-ray selected AGNs out to z=2.5, using far-IR data in three extragalacticdeep fields as part of the PACS Evolutionary Probe (PEP) program. Guided bystudies of intrinsic infra-red AGN SEDs, we show that the majority of the FIRemission in AGNs is produced by cold dust heated by star-formation. We uncovercharacteristic redshift-dependent trends between the mean FIR luminosity(L_fir) and accretion luminosity (L_agn) of AGNs. At low AGN luminosities,accretion and SFR are uncorrelated at all redshifts, consistent with a scenariowhere most low-luminosity AGNs are primarily fueled by secular processes intheir host galaxies. At high AGN luminosities, a significant correlation isobserved between L_fir and L_agn, but only among AGNs at low and moderateredshifts (z<1). We interpret this as a signature of the increasing importanceof major-mergers in driving both the growth of super-massive black holes(SMBHs) and global star-formation in their hosts at high AGN luminosities.However, we also find that the enhancement of SFR in luminous AGNs weakens ordisappears at high redshifts (z>1). This suggests that the role of mergers inSMBH-galaxy co-evolution is less important at these epochs. At all redshifts,we find essentially no relationship between L_fir and nuclear obscurationacross five orders of magnitude in obscuring column density, suggesting thatvarious different mechanisms are likely to be responsible for obscuring X-raysin active galaxies. We explain our results within a scenario in which twodifferent modes of SMBH fueling operate among low- and high-luminosity AGNs. Wepostulate, guided by emerging knowledge about the properties of high redshiftgalaxies, that the dominant mode of accretion among high-luminosity AGNsevolves with redshift.

The Mean Star Formation Rate of X-ray selected Active Galaxies and its Evolution from z=2.5: Results from PEP-Herschel