The evolution of a dense cold nuclear disc of gas, formed by inflowing stellar mass loss in a spherical galaxy, is investigated as a function of galaxy parameters. In all cases the disc growth, dominated by infall, continues until the onset of local gravitational instability close to the centre in a region within which the mean mass density p* is less than 104-105M. pc-3 . At this point massive star formation can propagate sequentially through the disc, leading to a burst of star formation. The viscosity of the disc is greatly enhanced and viscous inflow leads to nuclear activity either by accretion on to a massive black hole or by the formation of a massive central gas cloud. In the latter case the cloud is presumed to collapse to form either a black hole or a spinaL The theory imposes constraints on both the black hole and spinar models of nuclear activity_ On the black hole model, comparison with observations of galactic nuclei shows there can be little or no correlation between the mass of the hole and the luminosity of its accretion disc, and the hole must accrete only a very small fraction of the available fuel. On the spinar model the energy generation efficiency is much smaller and a larger proportion of the available fuel must be consumed by recurrent bursts of nuclear activity, each terminating in the explosive disruption of the central object. © Royal Astronomical Society • Provided by the NASA Astrophysics Data System.