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ABSTRACT A major open question in astrophysics is the mechanisms by which massive black holes (BHs) form in the early Universe, which pose constraints on seeding models. We study BH formation and evolution in a flexible model combining the cosmological IllustrisTNG (TNG) simulations with semi-analytic modelling in post-processing. We identify our TNG model hosts based on various criteria including a minimum gas mass of $10^7$$–$$10^9$${\rm M}_{\odot }$$, total host mass of $$10^{8.5}$$–$$10^{10.5}$${\rm M}_{\odot }$$, and a maximum gas metallicity of 0.01–0.1 $$\mathrm{Z}_{\odot }$$. Each potential host is assigned a BH seed with a probability of 0.01–1. The populations follow the TNG galaxy merger tree. This approach improves upon the predictive power of the simple TNG BH seeding prescription, narrowing down plausible seeding parameter spaces, and it is readily adaptable to other cosmological simulations. Several model realizations predict $$z\lesssim 4$$ BH mass densities that are consistent with empirical data as well as the TNG BHs. However, high-redshift BH number densities can differ by factors of $$\sim$$ 10 to $$\gtrsim$$ 100 between seeding parameters. In most model realizations, $$\lesssim 10^5$${\rm M}_{\odot }$$ BHs substantially outnumber heavier BHs at high redshifts. Mergers between such BHs are prime targets for gravitational-wave detection with Laser Interferometer Space Antenna. The $z=0$ BH mass densities in most realizations of the model agree well with observations, but our strictest seeding criteria fail at high redshift. Our findings strongly motivate the need for better empirical constraints on high-z BHs, and they underscore the significance of recent active galactic nucleus discoveries with JWST.