This paper presents a study of the distribution of massive dark objects (MDOs) in the centers of 36 nearby galaxies using Hubble Space Telescope photometry and ground-based kinematics. The models assume that each galaxy is axisymmetric with a two-integral distribution function, arbitrary inclination, and a position-independent stellar mass-to-light ratio. The models fit the kinematics of 32 galaxies for some value of MDO mass and mass-to-light ratio, while four galaxies have kinematically decoupled cores. The inferred mass-to-light ratios are consistent with the fundamental plane correlation $ \Upsilon \propto L^{0.2} $. For most galaxies, the MDO mass is found to be $ M_{\bullet} \sim 0.006M_{bulge} $, with five of six galaxies consistent with $ M_{\bullet} = 0 $ also fitting this correlation. The distribution of MDO masses is well described by a Gaussian distribution in $ \log(M_{\bullet}/M_{bulge}) $ with a mean of -2.27 and width of ~0.07. The results suggest that a large fraction of galaxies have MDOs, with a strong correlation between MDO mass and bulge mass. The study also considers various parameterizations for the probability distribution of MDO masses and finds that the best models indicate a high fraction of galaxies with MDOs. The results provide a first look at the statistical distribution of MDOs as a function of galaxy luminosity and other parameters.This paper presents a study of the distribution of massive dark objects (MDOs) in the centers of 36 nearby galaxies using Hubble Space Telescope photometry and ground-based kinematics. The models assume that each galaxy is axisymmetric with a two-integral distribution function, arbitrary inclination, and a position-independent stellar mass-to-light ratio. The models fit the kinematics of 32 galaxies for some value of MDO mass and mass-to-light ratio, while four galaxies have kinematically decoupled cores. The inferred mass-to-light ratios are consistent with the fundamental plane correlation $ \Upsilon \propto L^{0.2} $. For most galaxies, the MDO mass is found to be $ M_{\bullet} \sim 0.006M_{bulge} $, with five of six galaxies consistent with $ M_{\bullet} = 0 $ also fitting this correlation. The distribution of MDO masses is well described by a Gaussian distribution in $ \log(M_{\bullet}/M_{bulge}) $ with a mean of -2.27 and width of ~0.07. The results suggest that a large fraction of galaxies have MDOs, with a strong correlation between MDO mass and bulge mass. The study also considers various parameterizations for the probability distribution of MDO masses and finds that the best models indicate a high fraction of galaxies with MDOs. The results provide a first look at the statistical distribution of MDOs as a function of galaxy luminosity and other parameters.