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Binary black holes (BBHs) are thought to form in different environments, including the galactic field and (globular, nuclear, young and open) star clusters. Here, we propose a method to estimate the fingerprints of the main BBH formation channels associated with these different environments. We show that the metallicity distribution of galaxies in the local Universe along with the relative amount of mergers forming in the field or in star clusters determine the main properties of the BBH population. Our fiducial model predicts that the heaviest merger to date, GW170729, originated from a progenitor that underwent 2--3 merger events in a dense star cluster, possibly a galactic nucleus. The model predicts that at least one merger remnant out of 100 BBH mergers in the local Universe has mass $90 < M_{\rm rem}/ {\rm ~M}_\odot \leq{} 110$, and one in a thousand can reach a mass as large as $M_{\rm rem} \gtrsim 250$ M$_\odot$. Such massive black holes would bridge the gap between stellar-mass and intermediate-mass black holes. The relative number of low- and high-mass BBHs can help us unravelling the fingerprints of different formation channels. Based on the assumptions of our model, we expect that isolated binaries are the main channel of BBH merger formation if $\sim 70\%$ of the whole BBH population has remnants masses $75$ M$_\odot$ point to a significant sub-population of dynamically formed BBH binaries., 25 pages, 13 figures, 2 tables. Accepted for publication in the ApJ

The central region of the galaxy Henize 2-10 has a central black hole (BH) with a mass of about $2\times 10^6$ M$_\odot$. While this black hole does not appear to coincide with any central stellar over density, it is surrounded by 11 young massive clusters with masses above $10^5$ M$_\odot$. The availability of high quality data on the structure of the galaxy and the age and mass of the clusters provides excellent initial conditions for studying the dynamical evolution of Henize 2-10's nucleus. Here we present a set of $N$-body simulations of the central clusters and black hole to understand whether and how they will merge to form a nuclear star cluster. Nuclear star clusters (NSCs) are present in a majority of galaxies with stellar mass similar to Henize 2-10. Despite the results depend on the choice of initial conditions, we find that a NSC with mass $M_{NSC}\simeq 4-6\times 10^6$ M$_\odot$ and effective radius $r_{NSC}\simeq 2.6-4.1$ pc will form within $0.2$ Gyr. This work is the first showing, in a realistic realization of the host galaxy and its star cluster system, that the formation of a bright nucleus is a process that can happen after the formation of a central massive BH leading to a composite NSC+BH central system. The merging process of the clusters does not affect significantly the kinematics of the BH, whose motion, after the globular cluster merger, is limited to a $\sim 1$ pc oscillation at less than $2$ kms$^{-1}$ speed., 14 pages, 17 figures, 5 tables. Accepted for publication in the Astrophysical Journal