  We report a set of numerical experiments aimed at addressing the
applicability of competitive accretion to explain the high-mass end of the
stellar initial mass function in a sheet geometry with shallow gravitational
potential, in contrast to most previous simulations which have assumed
formation in a cluster gravitational potential. Our flat cloud geometry is
motivated by models of molecular cloud formation due to large-scale flows in
the interstellar medium. The experiments consisted of SPH simulations of gas
accretion onto sink particles formed rapidly from Jeans-unstable dense clumps
placed randomly in the finite sheet. These simplifications allow us to study
accretion with a minimum of free parameters, and to develop better statistics
on the resulting mass spectra. We considered both clumps of equal mass and
gaussian distributions of masses, and either uniform or spatially-varying gas
densities. In all cases, the sink mass function develops a power law tail at
high masses, with $dN/dlog M \propto M^{-\Gamma}$. The accretion rates of
individual sinks follow $\dot{M} \propto M^2$ at high masses; this results in a
continual flattening of the slope of the mass function towards an asymptotic
form $\Gamma \sim 1$ (where the Salpeter slope is $\Gamma = 1.35$). The
asymptotic limit is most rapidly reached when starting from a relatively broad
distribution of initial sink masses. In general the resulting upper mass slope
is correlated with the maximum sink mass; higher sink masses are found in
simulations with flatter upper mass slopes. Although these simulations are of a
highly idealized situation, the results suggest that competitive accretion may
be relevant in a wider variety of environments than previously considered, and
in particular that the upper mass distribution may generally evolve towards a
limiting value of $\Gamma \sim 1$.
