The rapid formation of supermassive black holes (SMBHs) at high redshifts is still a puzzle. One hypothesis is that intermediate-mass black holes (IMBHs) serve as seeds for their formation, which could arise from hierarchical mergers in dense star clusters. There are two possible pathways for IMBH formation: 1) very massive stars may form in young star clusters, such as Pop3 clusters, and evolve into IMBHs within a few million years; 2) multiple stellar-mass black holes can merge into IMBHs in dense nuclear star clusters. Detailed insights into these scenarios can be obtained through high-resolution star-by-star simulations of dense star clusters. Furthermore, upcoming observations of faint quasars, nuclear star clusters, and Pop3 stars with the James Webb Space Telescope (JWST) will offer valuable data to constrain theoretical models and deepen our understanding of the rapid formation of SMBHs.

In this contribution the hypothesis that the Galactic globular clusters with substantial internal [Fe/H] abundance ranges are the former nuclei of disrupted dwarf galaxies is discussed. Evidence considered includes the form of the metallicity distribution function, the occurrence of large diffuse outer envelopes in cluster density profiles, and the presence of ([s-process/Fe], [Fe/H]) correlations. The hypothesis is shown to be plausible but with the caveat that if significantly more than the current nine clusters known to have [Fe/H] spreads are found, then re-evaluation will be required.

Because of its nearness to Earth, the centre of the Milky Way is the only galaxy nucleus in which we can study the characteristics, distribution, kinematics, and dynamics of the stars on milli-parsec scales. We have accurate and precise measurements of the Galactic centre's central black hole, Sagittarius A*, and can study its interaction with the surrounding nuclear star cluster in detail. This contribution aims at providing a concise overview of our current knowledge about the Milky Way's central black hole and nuclear star cluster, at highlighting the observational challenges and limitations, and at discussing some of the current key areas of investigation.

There is a growing array of supermassive black hole and nuclear star cluster scaling relations with their host spheroid, including a bent (black hole mass)–(host spheroid mass) Mbh–Msph relation and a different (massive compact object mass)–(host spheroid velocity dispersion) Mmco–σ relations for black holes and nuclear star clusters. By combining the observed Mbh ∝ σ5.5 relation with the observed Mnc ∝ σ1.6–2.7 relation, we derive the expression Mbh ∝ Mnc2–3.4, which should hold until the nuclear star clusters are eventually destroyed in the larger core-Sérsic spheroids. This new mass scaling relation helps better quantify the rapid evolutionary growth of massive black holes in dense star clusters, and the relation is consistently recovered when coupling the observed Mnc ∝ Msph0.6–1.0 relation with the recently observed quadratic relation Mbh ∝ Msph2 for Sérsic spheroids.