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The processes that govern the formation of intermediate-mass black holes(IMBHs) in dense stellar clusters are still unclear. Here, we discuss the roleof stellar mergers, star-BH interactions and accretion, as well as BH binary(BBH) mergers in seeding and growing IMBHs in the \textsc{Dragon-II} simulationdatabase, a suite of 19 direct $N$-body models representing dense clusters withup to $10^6$ stars. \textsc{Dragon-II} IMBHs have typical masses of $m_{\rmIMBH} = (100-380)$ M$_\odot$ and relatively large spins $\chi_{\rm IMBH} >0.6$. We find a link between the IMBH formation mechanism and the clusterstructure. In clusters denser than $3\times 10^5$ M$_\odot$ pc$^{-3}$, thecollapse of massive star collision products represents the dominant IMBHformation process, leading to the formation of heavy IMBHs ($m_{\rm IMBH} >200$ M$_\odot$), possibly slowly rotating, that form over times $<5$ Myr andgrow further via stellar accretion and mergers in just $<30$ Myr. BBH mergersare the dominant IMBH formation channel in less dense clusters, for which wefind that the looser the cluster, the longer the formation time ($10-300$ Myr)and the larger the IMBH mass, although remaining within $200$ M$_\odot$. Strongdynamical scatterings and relativistic recoil efficiently eject all IMBHs in\textsc{Dragon-II} clusters, suggesting that IMBHs in this type of cluster areunlikely to grow beyond a few $10^2$ M$_\odot$.

The Dragon-II simulations -- II. Formation mechanisms, mass, and spin of intermediate-mass black holes in star clusters with up to 1 million stars