We investigate the link between a galaxy's SFR and the accretion rate of its central BH as predicted by the EAGLE simulations of galaxy evolution. Contrary to the original concept that galaxy bulge and BH mass correlate tightly with a roughly linear relation, EAGLE finds three distinct trends of BH and galaxy mass over three distinct ranges of halo/stellar mass. This adapts this single relation, to three: BHs hosted within low mass haloes fail to grow beyond their inception mass as their halo is regulated efficiently via stellar feedback; in intermediate mass haloes this stellar feedback becomes inefficient and BH growth becomes non-linear creating a steep relation between BH and galaxy mass; finally, in high mass haloes, further growth is regulated via efficient AGN feedback and the relation now shallows. Each regime has a serious consequence on how BHAR and SFR are linked, depending now on the evolutionary stage of the halo. We investigate if this behaviour could be observed and as to the nature of what ultimately fuels the process of both BH and galaxy growth.