  We study a simplified model for pulsed laser deposition [Phys. Rev. Lett.
{\bf 87}, 135701 (2001)] by rate equations. We consider a set of equations,
where islands are assumed to be point-like, as well as an improved one that
takes the size of the islands into account. The first set of equations is
solved exactly but its predictive power is restricted to a few pulses. The
improved set of equations is integrated numerically, is in excellent agreement
with simulations, and fully accounts for the crossover from continuous to
pulsed deposition. Moreover, we analyze the scaling of the nucleation density
and show numerical results indicating that a previously observed logarithmic
scaling does not apply.
