  We model the inspiral of globular clusters (GCs) towards a galactic nucleus
harboring a supermassive black hole (SMBH), a leading scenario for the
formation of nuclear star clusters. We consider the case of GCs containing
either an intermediate-mass black hole (IMBH) or a population of stellar mass
black holes (BHs), and study the formation of gravitational wave (GW) sources.
We perform direct summation $N$-body simulations of the infall of GCs with
different orbital eccentricities in the live background of a galaxy with either
a shallow or steep density profile. We find that the GC acts as an efficient
carrier for the IMBH, facilitating the formation of a bound pair. The hardening
and evolution of the binary depends sensitively on the galaxy's density
profile. If the host galaxy has a shallow profile the hardening is too slow to
allow for coalescence within a Hubble time, unless the initial cluster orbit is
highly eccentric. If the galaxy hosts a nuclear star cluster, the hardening
leads to coalescence by emission of GWs within $3-4$ Gyr. In this case, we find
a 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 are
deposited close enough to the SMBH to form extreme-mass-ratio-inspirals with a
merger rate of $\Gamma_{\rm EMRI} = 0.25$ yr$^{-1}$ Gpc$^{-3}$. Finally, the
SMBH tidal field can boost the coalescence of stellar black hole binaries
delivered from the infalling GCs. The merger rate for this merging channel is
$\Gamma_{\rm BHB} = 0.4-4$ yr$^{-1}$ Gpc$^{-3}$.
