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During their evolution, star clusters undergo mass segregation, by which theorbits of the most massive stars shrink, while the lighter stars move outwardsfrom the cluster centre. In this context, recent observations and dynamicalmodelling of several galactic and extra-galactic globular clusters (GCs)suggest that most of them show, close to their centre, an overabundance of masswhose nature is still matter of debate. For instance, many works show thatorbitally segregated stars may collide with each other in a runaway fashion,leading to the formation of a very massive star or an intermediate mass blackhole (IMBH) with a mass comparable to the observed mass excess. On the otherhand, segregated stars can form a dense system if the IMBH formation fails. Inthis paper we study the early formation phase of a dense, massive sub-system(MSS) in several GCs models using a recently developed semi-analyticaltreatment of the mass segregation process. In order to investigate how the MSSproperties depend on the host cluster properties, we varied initial massfunction (IMF), total mass, spatial distribution and metallicity of our models.Our results show how the IMF contributes to determine the final mass of theMSS, while the metallicity and the spatial distribution play a minor role. Themethod presented in this paper allowed us to provide scaling relations thatconnect the MSS mass and the host cluster mass in agreement with the observedcorrelation. In order to follow the early formation stage of the MSSs andimprove our statistical results, we performed several $N$-body simulations ofstellar clusters with masses between $10^3$ and $2\times 10^5$ solar masses.

On the formation of compact, massive sub-systems in stellar clusters and its relation with intermediate mass black holes