  We explore the idea that the power-law tail in the mass function of
protostellar condensations and stars arises from the accretion of ambient cloud
material on to a condensation, coupled with a nonuniform (exponential)
distribution of accretion lifetimes. This model allows for the generation of
power-law distributions in all star-forming regions, even if condensations
start with a lognormal mass distribution, as may be expected from the central
limit theorem, and supported by some recent numerical simulations of turbulent
molecular clouds. For a condensation mass $m$ with growth rate $dm/dt \propto
m$, an analytic three-parameter probability density function is derived; it
resembles a lognormal at low mass and has a pure power-law high-mass tail. An
approximate power-law tail is also expected for other growth laws, and we
calculate the distribution for the plausible case $dm/dt \propto m^{2/3}$.
Furthermore, any single time snapshot of the masses of condensations that are
still accreting (and are of varying ages) also yields a distribution with a
power-law tail similar to that of the IMF.
