  We present results for collective diffusion of adatoms on a stepped substrate
with a submonolayer coverage. We study the combined effect of the additional
binding at step edge, the Schwoebel barrier, the enhanced diffusion along step
edges, and the finite coverage on diffusion as a function of step density. In
particular, we examine the crossover from step--dominated diffusion at high
step density to terrace-dominated behavior at low step density in a lattice-gas
model using analytical Green's function techniques and Monte Carlo simulations.
The influence of steps on diffusion is shown to be more pronounced than
previously anticipated.
