  We study the relation of AGN accretion, star formation rate (SFR), and
stellar mass (M$_*$) using a sample of $\approx$ 8600 star-forming galaxies up
to z=2.5 selected with \textit{Herschel} imaging in the GOODS and COSMOS
fields. For each of them we derive SFR and M$_*$, both corrected, when
necessary, for emission from an active galactic nucleus (AGN), through the
decomposition of their spectral energy distributions (SEDs). About 10 per cent
of the sample are detected individually in \textit{Chandra} observations of the
fields. For the rest of the sample we stack the X-ray maps to get average X-ray
properties. After subtracting the X-ray luminosity expected from star formation
and correcting for nuclear obscuration, we derive the average AGN accretion
rate for both detected sources and stacks, as a function of M$_{*}$, SFR and
redshift. The average accretion rate correlates with SFR and with M$_*$. The
dependence on SFR becomes progressively more significant at z$>$0.8. This may
suggest that SFR is the original driver of these correlations. We find that
average AGN accretion and star formation increase in a similar fashion with
offset from the star-forming "main-sequence". Our interpretation is that
accretion onto the central black hole and star formation broadly trace each
other, irrespective of whether the galaxy is evolving steadily on the
main-sequence or bursting.
