  The origin and properties of the initial black hole seeds that grow to
produce the observed population of accreting sources remain to be determined.
It is a challenge to uniquely disentangle signatures of seeding from fueling
and dynamics that shapes the assembly history of growing black holes. To
address this, we use a semi-analytic model developed to track the growth of
supermassive black holes adopting multiple prescriptions for accretion. In
contrast with earlier treatments, we explore the interplay between seeding
models and two accretion modes. We find that signatures of the initial seeding
do survive in the following observational probes: the black hole occupation
fraction; contribution to the unresolved X-ray background; low-luminosity and
high-redshift luminosity functions; and in gravitational wave event signatures.
We find that the behaviour of the low-mass end of the M-sigma relation is
dominated by uncertainties in the adopted accretion prescriptions and does not
offer clear discrimination between seeding models. We make concrete predictions
for future surveys, particularly for the Lynx X-ray surveyor and LISA (The
Laser Interferometer Space Antenna) mission, which will each provide different
and yet strong constraints on the seed population. Black hole coalescences
detected by LISA and high-redshift quasar luminosity functions observed by Lynx
will offer the sharpest seeding discriminants. Although the signatures of the
black hole seeding mechanism that persist remain linked to our understanding of
black hole accretion and dynamics, we offer new insights on how these upcoming
multi-wavelength observations could be leveraged to effectively disentangle
them.
