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We investigate the formation of intermediate mass black holes (IMBHs) throughhierarchical mergers of stellar origin black holes (BHs), as well as BH mergersformed dynamically in nuclear star clusters. Using a semi-analytical approachwhich incorporates probabilistic mass-function-dependent double BH (DBH)pairing, binary-single encounters, and a mass-ratio-dependent prescription forenergy dissipation in hardening binaries, we find that IMBHs with masses of$O(10^2)$-$O(10^4)\rm M_\odot$ can be formed solely through hierarchicalmergers in timescales of a few $100$ Myrs to a few Gyrs. Clusters with escapevelocities $\gtrsim400$ km s$^{-1}$ inevitably form high-mass IMBHs. The spindistribution of IMBHs with masses $\gtrsim 10^3$ M$_\odot$ is stronglyclustered at $\chi\sim 0.15$; while for lower masses, it peaks at $\chi\sim0.7$. Eccentric mergers are more frequent for equal-mass binaries containingfirst-and/or second-generation BHs. Metal-rich, young, dense clusters canproduce up to $20\%$ of their DBH mergers with eccentricity $\geq0.1$ at$10\,\rm Hz$, and $\sim2$-$9\%$ of all in-cluster mergers can form at $>10$ Hz.Nuclear star clusters are therefore promising environments for the formation ofhighly-eccentric DBH mergers, detectable with current gravitational-wavedetectors. Clusters of extreme mass ($\sim10^8$ M$_\odot$) and density($\sim10^8$ M$_\odot$pc$^{-3}$) can have about half of all of their DBH mergerswith primary masses $\geq100$ M$_\odot$. The fraction of in-cluster mergersincreases rapidly with increasing cluster escape velocity, being nearly unityfor $v_{\rm esc}\gtrsim 200$ km s$^{-1}$. Cosmological merger rate of DBHs fromnuclear clusters varies $\lessapprox0.01-1$ Gpc$^{-3}$yr$^{-1}$.

Double black hole mergers in nuclear star clusters: eccentricities, spins, masses, and the growth of massive seeds