  (ABRIDGED) We present a model in which the seeds of supermassive black holes
form from the lowest angular momentum gas in proto-galaxies at high redshift.
We show that this leads to a correlation between black hole masses and spheroid
properties, as observed today. We assume that gas in early-forming, rare halos
has a distribution of specific angular momentum similar to that expected for
dark matter halos. This distribution has a significant low angular momentum
tail which implies that every proto-galaxy should contain gas that ends up in a
high-density disc. In halos more massive than a critical threshold of
\~10^8Msun, the discs are gravitationally unstable, and experience an efficient
Lin-Pringle viscosity that allows mass inflow. This process continues until the
first massive stars disrupt the disc. Black holes are created with a
characteristic mass of ~10^5 Msun, independent of the redshift of formation.
This serves as a lower bound for black-hole masses in galaxies today. The
comoving mass density of black hole seeds grows with time, and saturates when
cosmic reionization stops gas cooling in these low-mass systems. By z~15, the
comoving mass density becomes comparable to that inferred from observations,
with room for appropriate additional luminous growth during a later quasar
accretion phase. Hierarchical merging after z~15 naturally leads to a linear
correlation between black-hole mass and stellar spheroid mass, with negligible
black hole masses in disc-dominated galaxies.
