Two-dimensional calculations of the hydrodynamics produced by nuclear starbursts, taking into consideration the accretion or infall of disk matter on to the heart of the starburst, are here shown to lead to stationary solutions that naturally account for the kpc-scale biconical X-ray and optically detected filamentary structure. The calculated flows are critically compared with former models and with observations of nuclear starbursts. For the infall models, we find that the mechanical energy power of the nuclear cluster must exceed a threshold value, imposed by the rate of disk mass accretion, to undergo blowout. This, combined with an initial mass function, is shown to regulate the minimum amount of mass that a starburst needs to generate kpc-scale outflows.