We use semi-analytic models implemented in the Millennium Simulation to analyze the merging histories of dark matter haloes and of the galaxies that reside in them. We assume that supermassive black holes only exist in galaxies that have experienced at least one major merger. Only a few percent of galaxies with stellar masses less than $M_* < 10^{10} M_{odot}$ are predicted to have experienced a major merger and to contain a black hole. The fraction of galaxies with black holes increases very steeply at larger stellar masses. This agrees well with the observed strong mass dependence of the fraction of nearby galaxies that contain either low-luminosity (LINER-type) or higher-luminosity (Seyfert or composite-type) AGN. We then investigate when the major mergers that first create the black holes are predicted to occur. High mass galaxies are predicted to have formed their black holes at very early epochs. The majority of low mass galaxies never experience a major merger and hence do not contain a black hole, but a significant fraction of the supermassive black holes that do exist in low mass galaxies are predicted to have formed recently.
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