We investigate the impact of different initial conditions for the initial density profile and the initial turbulence on the formation process of protostellar clusters. We study the collapse of dense molecular cloud cores with three-dimensional adaptive mesh refinement simulations. We focus our discussion on the distribution of the gas among the protostellar objects in the turbulent dynamical cores. Despite the large variations in the initial configurations and the resulting gas and cluster morphology we find that all stellar clusters follow a very similar gas accretion behaviour. Once secondary protostars begin to form, the central region of a cluster is efficiently shielded from further accretion. Hence, objects located close to the centre are starved of material, as indicated by a strong decrease of the central accretion rate. This fragmentation-induced starvation occurs not only in rotationally supported discs and filaments, but also in more spherically symmetric clusters with complex chaotic motions.