Figure 7: (a) Mass function of seed black holes predicted by the model based on (14) and (15). The black solid line refers to , while the red line refers to . The long-dashed line shows the effect of reducing from 2 to 1.5. The short dashed line shows the effect of not including the possibility of fragmentation (more details can be found in [14]). (b) The integrated density of black holes predicted from a merger tree evolution of the black hole seed population. The three solid lines refer to three different choices of the parameters (see [15] for details). The dashed area indicates the observationally permitted region from estimates of the black hole density at low redshifts. At high redshift ( ), the density reflects the one attained after the seed formation phase, while the rise at lower redshifts indicates the growth through AGN activity.