ABSTRACT The observed super-massive black hole (SMBH) mass–galaxy velocity dispersion (Mbh–) correlation may be established when winds/outflows from the SMBH drive gas out of the potential wells of classical bulges. Here we present numerical simulations of this process in a static isothermal potential. Simple spherically symmetric models of SMBH feedback at the Eddington luminosity can successfully explain the Mbh– and nuclear cluster mass MNC– correlations, as well as why larger bulges host SMBH while smaller ones host nuclear star clusters. However, these models do not specify how SMBH feed on infalling gas whilst simultaneously producing feedback that drives gas out of the galaxy. More complex models with rotation and/or anisotropic feedback allow SMBH to feed via a disc or regions not exposed to SMBH winds, but in these more realistic cases it is not clear why a robust Mbh– relation should be established. In fact, some of the model predictions contradict observations. For example, an isotropic SMBH wind impacting on a disc (rather than a shell) of aspect ratio H/R≪ 1 requires the SMBH mass to be larger by a factor of ∼R/H, which is opposite to what is observed. We conclude that understanding how an SMBH feeds is as important a piece of the puzzle as understanding how its feedback affects its host galaxy. Finally, we note that in aspherical cases the SMBH outflows induce differential motions in the bulge. This may pump turbulence that is known to hinder star formation in star-forming regions. SMBH feedback thus may not only drive gas out of the bulge but also reduce the fraction of gas turned into stars.