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We explore the properties of dense star clusters that are likely to be thenurseries of stellar black holes pairing in close binaries. We combine acosmological model of globular cluster formation with analytic prescriptionsfor the dynamical assembly and evolution of black hole binaries to constrainwhich types of clusters are most likely to form binaries tight enough tocoalesce within a Hubble time. We find that black hole binaries which areejected and later merge ex-situ form in clusters of a characteristic mass$M_{\rm cl} \sim 10^{5.3}M_{\odot}$, whereas binaries which merge in-situ formin more massive clusters, $M_{\rm cl} \sim 10^{5.7}M_{\odot}$. The clusterswhich dominate the production of black hole binaries are similar in age andmetallicity to the entire population. Finally, we estimate an approximatecosmic black hole merger rate of dynamically assembled binaries using the meanblack hole mass for each cluster given its metallicity. We find an intrinsicrate of $\sim 6\,\mathrm{Gpc\,yr^{-1}}$ at $z=0$, a weakly increasing mergerrate out to $z=1.5$, and then a decrease out to $z=4$. Our results can be usedto provide a cosmological context and choose initial conditions in numericalstudies of black hole binaries assembled in star clusters.

The star clusters that make black hole binaries across cosmic time