  We use a suite of hydrodynamical simulations of galaxy mergers to compare
star formation rate (SFR) and black hole accretion rate (BHAR) for galaxies
before the interaction ('stochastic' phase), during the `merger' proper,
lasting ~0.2-0.3 Gyr, and in the `remnant' phase. We calculate the bi-variate
distribution of SFR and BHAR and define the regions in the SFR-BHAR plane that
the three phases occupy. No strong correlation between BHAR and galaxy-wide SFR
is found. A possible exception are galaxies with the highest SFR and the
highest BHAR. We also bin the data in the same way used in several
observational studies, by either measuring the mean SFR for AGN in different
luminosity bins, or the mean BHAR for galaxies in bins of SFR. We find that the
apparent contradiction or SFR versus BHAR for observed samples of AGN and star
forming galaxies is actually caused by binning effects. The two types of
samples use different projections of the full bi-variate distribution, and the
full information would lead to unambiguous interpretation. We also find that a
galaxy can be classified as AGN-dominated up to 1.5 Gyr after the merger-driven
starburst took place. Our study is consistent with the suggestion that most
low-luminosity AGN hosts do not show morphological disturbances.
