ABSTRACT We investigate the co-evolution of the black hole accretion rate (BHAR) and the star formation rate (SFR) in galaxies displaying a greater diversity of star-forming properties compared to previous studies. We combine X-ray stacking and far-IR photometry of stellar mass-limited samples of normal star-forming, starburst, and quiescent/quenched galaxies in the COSMOS field. We corroborate the existence of a strong correlation between BHAR (i.e., the X-ray luminosity, LX) and stellar mass (M*) for normal star-forming galaxies, though we find a steeper relation than previously reported. We find that starbursts show a factor of three enhancement in BHAR compared to normal SF galaxies (against a factor of six excess in SFR), while quiescents show a deficit of a factor times 5.5 at a given mass. One possible interpretation of this is that the starburst phase does not coincide with cosmologically relevant BH growth, or that starburst-inducing mergers are more efficient at boosting SFR than BHAR. Contrary to studies based on smaller samples, we find that the BHAR/SFR ratio of main-sequence (MS) galaxies is not mass invariant, but scales weakly as , implying faster BH growth in more massive galaxies at . Furthermore, BHAR/SFR during the starburst is a factor of two lower than in MS galaxies, at odds with the predictions of hydrodynamical simulations of merger galaxies that foresee a sudden enhancement of LX/SFR during the merger. Finally, we estimate that the bulk of the accretion density of the universe at is associated with normal star-forming systems, with only and associated with starburst and quiescent galaxies, respectively.