tokens: the peak of the distribution to larger distances, from ≈5 kpc in the smallest galaxy considered here to ≈12 kpc in the largest galaxy. We note that GC distributions tend to be broader around the peak of their number distributions in elliptical galaxies relative to spiral galaxies, in which they appear more concentrated around the peak. The Sérsic index slightly affects the cluster distribution (the lower the n , the smaller the peak distance), but it has a negligible effect on the final number of GCs. Figure 2. Radial distribution of surviving GCs (with IMBH in their centers) in early-type galaxies (left) and late-type galaxies (right) with stellar mass (top), (center) and (bottom), for different Sérsic indexes. Figure 3. The final cumulative radial distribution of IMBHs in star clusters in different early-type galaxies (top) and late-type galaxies (bottom), and different Sérsic indexes. 5. TDEs We calculate the TDE rates by IMBHs in GCs in two limiting cases: one in which a density cusp cannot form due to a rapid depletion by TDEs and one in which a density cusp of stars with total mass M IMBH forms around the IMBH. In both cases, we take into account the stars accreted by the IMBH and remove stars from the host GC every time they undergo a TDE. The tidal disruption of a star by an IMBH occurs when a star on an eccentric orbit has an angular momentum smaller than the so-called loss-cone angular momentum (Peebles 1972 ; Bahcall Wolf 1976 ; Lightman Shapiro 1977 ; Baumgardt et al. 2006 )whereis the tidal disruption radius of a star of mass m * and radius R * . Within the IMBH radius of influencewhere is the velocity dispersion in the cluster core, the dynamics is dominated by the IMBH gravitational potential. Nevertheless, stars exchange energy and angular momentum through two-body interactions on the typical relaxation timescalewhere Λ is a dimensionless constant of order unity (which contains the Coulomb logarithm), and and are the velocity dispersion and density at semimajor axis a , respectively. As a consequence of the numerous small-angle two-body deflections, a star with energy E and angular momentum J will diffuse in E – J space (for a comprehensive review see Alexander 2017 , and references therein). Being a random-walk process, the change in angular momentum in a time is ( J c is the angular momentum of a circular orbit with the same a ), which implies a typical timescalewhere e is the eccentricity of the star, to change the angular momentum to be of order J . Thus, more eccentric orbits relax more rapidly than circular orbits at the same a . If (empty loss-cone regime), any star deflected into the loss-cone is disrupted within a dynamical time, while if (full loss-cone regime), stars may be scattered in and out of the loss-cone on their way from apoapse to periapse (Baumgardt et al. 2004a , 2004b , 2005 ). After a rapid initial phase characterized by the wandering of the IMBH through a sea of stars (Chatterjee et al. 2002a , 2002b
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