The assembly of intermediate black holes with complementary approaches: Dragon II and BPop

Intermediate-mass black holes (IMBHs) occupy the $10^2 - 10^5\,M_\odot$ range, but their existence remains poorly constrained. Only a few candidates have been suggested in dwarf galaxies, globular clusters, and LIGO-Virgo-Kagra detections. To investigate their formation and demographics, we adopt two complementary approaches. We first analyze the \textsc{dragonii} direct $N$-body simulations, which follow clusters with up to $10^6$ stars, capture IMBHs growth. We then employ the semi-analytic code \textsc{bpop}, calibrated on \textsc{dragonii}, to explore a broad range of cluster and cosmological conditions. Our models reproduce merger rates consistent with GWTC-3, with $\sim30 - 60\%$ of BBHs forming dynamically, mainly in globular and nuclear clusters. About 2-3\% of mergers involve an IMBH, producing intermediate-mass ratio inspirals. The IMBH mass distribution spans $2.5 \times 10^2 - 4 \times 10^4\,M_\odot$, with rare growth beyond $10^6\,M_\odot$. Formation efficiency rises with initial binary fraction but declines in metal-rich environments. IMBHs thus emerge as a distinct population bridging stellar and supermassive black holes.