Massive black hole seeds from low angular momentum material

(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.