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We calculate cosmic distributions in space and time of the formation sites ofthe first, "Pop III.1" stars, exploring a model in which these are theprogenitors of all supermassive black holes (SMBHs), seen in the centers ofmost large galaxies. Pop III.1 stars are defined to form from primordialcomposition gas in dark matter minihalos with $\sim10^6\:M_\odot$ that areisolated from neighboring astrophysical sources by a given isolation distance,$d_{\rm{iso}}$. We assume Pop III.1 sources are seeds of SMBHs, based onprotostellar support by dark matter annihilation heating that allows them toaccrete a large fraction of their minihalo gas, i.e., $\sim10^5\:M_\odot$.Exploring $d_{\rm{iso}}$ from $10 - 100\:\rm{kpc}$ (proper distances), wepredict the redshift evolution of Pop III.1 source and SMBH remnant numberdensities. The local, $z=0$ density of SMBHs constrains $d_{\rm{iso}}\lesssim100\:\rm{kpc}$ (i.e., $3\:\rm{Mpc}$ comoving distance at $z\simeq30$). In oursimulated ($\sim60\:\rm{Mpc}$)$^3$ comoving volume, Pop III.1 stars startforming just after $z=40$. Their formation is largely complete by $z\simeq25$to $20$ for $d_{\rm{iso}}=100$ to $50\:\rm{kpc}$. We follow source evolution to$z=10$, by which point most SMBHs reside in halos with $\gtrsim10^8\:M_\odot$.Over this period, there is relatively limited merging of SMBHs for these valuesof $d_{\rm{iso}}$. We also predict SMBH clustering properties at $z=10$:feedback suppression of neighboring sources leads to relatively flat angularcorrelation functions.

The Formation of Supermassive Black Holes from Population III.1 Seeds. I. Cosmic Formation Histories and Clustering Properties