  We present a model to explain the mass segregation and shallow mass functions
observed in the central parts of dense and young starburst stellar clusters.
The model assumes that the initial pre-stellar cores mass function resulting
from the turbulent fragmentation of the proto-cluster cloud is significantly
altered by the cores coalescence before they collapse to form stars. With
appropriate, yet realistic parameters, this model based on the competition
between cores coalescence and collapse reproduces the mass spectra of the well
studied Arches cluster. Namely, the slopes at the intermediate and high mass
ends are reproduced, as well as the peculiar bump observed at 6 M_sol. This
coalescence-collapse process occurs on short timescale of the order of one
fourth the free fall time of the proto-cluster cloud (i.e., a few 10^{4}
years), suggesting that mass segregation in Arches and similar clusters is
primordial. The best fitting model implies the total mass of the Arches cluster
is 1.45 10^{5} M_sol, which is slightly higher than the often quoted, but
completeness affected, observational value of a few 10^{4} M_sol. The derived
star formation efficiency is ~30 percent which implies that the Arches cluster
is likely to be gravitationally bound.
