  We study the diffusion and submonolayer spreading of chainlike molecules on
surfaces. Using the fluctuating bond model we extract the collective and tracer
diffusion coefficients D_c and D_t with a variety of methods. We show that
D_c(theta) has unusual behavior as a function of the coverage theta. It first
increases but after a maximum goes to zero as theta go to one. We show that the
increase is due to entropic repulsion that leads to steep density profiles for
spreading droplets seen in experiments. We also develop an analytic model for
D_c(theta) which agrees well with the simulations.
