Identifying the processes that determine strength, duration and variability of protostellar mass growth is a fundamental ingredient of any theory of star formation. I discuss protostellar mass accretion rates dM/dt from numerical models which follow molecular cloud evolution from turbulent fragmentation towards the formation of stellar clusters. In a dense cluster environment, dM/dt is strongly time varying and influenced by the mutual interaction of protostellar cores and their competition for accretion from the common cluster gas reservoir. Even for protostars with similar final mass, the accretion histories may differ dramatically. High-mass stars build up in the central parts of dense, cluster-forming cloud regions. They begin to form in the early phases of cluster evolution, and continue to grow at a high rate until the available gas is exhausted or expelled by feedback. Lower-mass stars tend to form at later phases, and dM/dt declines rapidly after a short initial phase of strong growth. I present a simple fit formula for the time evolution of the average dM/dt for protostars of different masses in a dense cluster environment.

ApJ Letters in press, 4 pages including 2 resolution-reduced figures, full resolution version available at http://www.ucolick.org/~ralf/Preprints/p11.abstract.html