  We present an implementation of Pop III.1 seeding of supermassive black holes
(SMBHs) in a theoretical model of galaxy formation and evolution to assess the
growth the SMBH population and the properties of the host galaxies. The model
of Pop III.1 seeding involves SMBH formation at redshifts $z\gtrsim 20$ in dark
matter minihalos that are isolated from external radiative feedback,
parameterized by isolation distance $d_{\rm iso}$. Within a standard
$\Lambda$CDM cosmology, we generate dark matter halos using the code
\textsc{pinocchio} and seed them according to the Pop III.1 scenario, exploring
values of $d_{\rm iso}$ from 50 to 100~kpc (proper distance). We consider two
alternative cases of SMBH seeding: a Halo Mass Threshold (HMT) model in which
all halos $>7\times10^{10}\:M_\odot$ are seeded with $\sim 10^5\:M_\odot$ black
holes; an All Light Seed (ALS) model in which all halos are seeded with low,
stellar-mass black holes. We follow the redshift evolution of the halos,
populating them with galaxies using the GAlaxy Evolution and Assembly
theoretical model of galaxy formation, including accretion on SMBHs and related
feedback processes. Here we present predictions for the properties of galaxy
populations, focusing on stellar masses, star formation rates, and black hole
masses. The local, $z\sim0$ metrics of occupation fraction as a function of the
galaxy stellar mass, galaxy stellar mass function (GSMF), and black hole mass
function (BHMF) all suggest a constraint of $d_{\rm iso}<75\:$kpc. We discuss
the implications of this result for the Pop III.1 seeding mechanism.
