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ABSTRACT  Galactic nuclei host central massive objects either in the form of supermassive black holes or in the form of nuclear stellar clusters. Recent investigations have shown that both components co‐exist in at least a few galaxies. In this paper, we explore the possibility of a connection between nuclear star clusters and black holes that establishes at the moment of their formation. We here model the evolution of high‐redshift discs, hosted in dark matter haloes with virial temperatures &gt; 10 4   K, whose gas has been polluted with metals just above the critical metallicity for fragmentation. A nuclear cluster forms as a result of a central starburst from gas inflowing from the unstable disc. The nuclear stellar cluster provides a suitable environment for the formation of a black hole seed, ensuing from runaway collisions among the most massive stars. Typical masses for the nuclear stellar clusters at the time of black hole formation (  z ∼ 10 ) are in the range  10 4 –10 6  M ⊙   and have half‐mass radii  ≲ 0.5 pc. The black holes forming in these dense, high‐redshift clusters can have masses in the range  ∼  300–2000 M ⊙  .

High‐redshift formation and evolution of central massive objects – I. Model description