There is accumulating evidence for a strong link between nuclear starbursts and AGN. Molecular gas in the central regions of galaxies plays a critical role in fueling nuclear starburst activity and feeding central AGN. The dense molecular ISM is accreted to the nuclear regions by stellar bars and galactic interactions. Here we describe recent observational results for the OB star forming regions in M51 and the nuclear star burst in Arp 220 - both of which have approximately the same rate of star formation per unit mass of ISM. We suggest that the maximum efficiency for forming young stars is an Eddington-like limit imposed by the radiation pressure of newly formed stars acting on the interstellar dust. This limit corresponds to approximately 500 $L_{igodot} / M_{igodot}$ for optically thick regions in which the radiation has been degraded to the NIR. Interestingly, we note that some of the same considerations can be important in AGN where the source of fuel is provided by stellar evolution mass-loss or ISM accretion. Most of the stellar mass-loss occurs from evolving red giant stars and whether their mass-loss can be accreted to a central AGN or not depends on the radiative opacity of the mass-loss material. The latter depends on whether the dust survives or is sublimated (due to radiative heating). This, in turn, is determined by the AGN luminosity and the distance of the mass-loss stars from the AGN. Several AGN phenomena such as the broad emission and absorption lines may arise in this stellar mass-loss material. The same radiation pressure limit to the accretion may arise if the AGN fuel is from the ISM since the ISM dust-to-gas ratio is the same as that of stellar mass-loss.