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We present predictions for cosmic evolution of populations of supermassive black holes (SMBHs) forming from Population III.1 seeds, i.e. early, metal-free dark matter minihaloes forming far from other sources, parametrized by isolation distance, d iso. Extending previous work that explored this scenario to z  = 10, we follow evolution of a |$(60\, {\rm {Mpc}})^3$| volume to z  = 0. We focus on evolution of SMBH comoving number densities, halo occupation fractions, angular clustering, and 3D clustering, exploring a range of d iso constrained by observed local number densities of SMBHs. We also compute synthetic projected observational fields, in particular, a case comparable to the Hubble Ultra Deep Field. We compare Pop III.1 seeding to a simple halo mass threshold model, commonly adopted in cosmological simulations of galaxy formation. Major predictions of the Pop III.1 model include that all SMBHs form by z ∼ 25, after which their comoving number densities are near-constant, with low merger rates. Occupation fractions evolve to concentrate SMBHs in the most massive haloes by z  = 0, but with rare cases of SMBHs in haloes down to |$\sim 10^8\, M_\odot$|⁠. The d iso scale at epoch of formation, e.g. |$100\,$| kpc-proper at z ∼ 30, i.e. |$\sim 3\,$| Mpc-comoving, is imprinted in the SMBH two-point angular correlation function, remaining discernible as a low-amplitude feature to z ∼ 1. The SMBH 3D two-point correlation function at z  = 0 also shows lower amplitude compared to equivalently massive haloes. We discuss prospects for testing these predictions with observational surveys of SMBH populations. [ABSTRACT FROM AUTHOR]