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We model the inspiral of globular clusters (GCs) towards a galactic nucleusharboring a supermassive black hole (SMBH), a leading scenario for theformation of nuclear star clusters. We consider the case of GCs containingeither an intermediate-mass black hole (IMBH) or a population of stellar massblack holes (BHs), and study the formation of gravitational wave (GW) sources.We perform direct summation $N$-body simulations of the infall of GCs withdifferent orbital eccentricities in the live background of a galaxy with eithera shallow or steep density profile. We find that the GC acts as an efficientcarrier for the IMBH, facilitating the formation of a bound pair. The hardeningand evolution of the binary depends sensitively on the galaxy's densityprofile. If the host galaxy has a shallow profile the hardening is too slow toallow for coalescence within a Hubble time, unless the initial cluster orbit ishighly eccentric. If the galaxy hosts a nuclear star cluster, the hardeningleads to coalescence by emission of GWs within $3-4$ Gyr. In this case, we finda IMBH-SMBH merger rate of $\Gamma_{\rm IMBH-SMBH} = 2.8\times 10^{-3}$yr$^{-1}$ Gpc$^{-3}$. If the GC hosts a population of stellar BHs, these aredeposited close enough to the SMBH to form extreme-mass-ratio-inspirals with amerger rate of $\Gamma_{\rm EMRI} = 0.25$ yr$^{-1}$ Gpc$^{-3}$. Finally, theSMBH tidal field can boost the coalescence of stellar black hole binariesdelivered from the infalling GCs. The merger rate for this merging channel is$\Gamma_{\rm BHB} = 0.4-4$ yr$^{-1}$ Gpc$^{-3}$.

Gravitational wave sources from inspiralling globular clusters in the Galactic Centre and similar environments