I present a model to explain the mass segregation and shallow mass functions observed in the central parts of 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, as well as the peculiar bump observed at $6M_{igodot}$. This coalescence-collapse process occurs on a short timescale of the order of 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 $1.45{ imes}10^5M_{igodot}$, which is slightly higher than the often quoted, but completeness affected, observational value of a few $10^4M_{igodot}$. The model implies a star formation efficiency of ${sim}30$ percent which implies that the Arches cluster is likely to a gravitationally bound system.