Pulsed laser deposition (PLD) is a popular growth method, which has been successfully used for fabricating thin films. Compared to continuous deposition (like molecular beam epitaxy) the pulse intensity can be used as an additional parameter for tuning the growth behavior, so that under certain circumstances PLD improves layer-by-layer growth. We present kinetic Monte-Carlo simulations for PLD in the submonolayer regime and give a description of the island distance versus intensity. Furthermore we discuss a theory for second layer nucleation and the impact of Ehrlich-Schwoebel barriers on the growth behavior. We find an exact analytical expression for the probability of second layer nucleation during one pulse for high Ehrlich-Schwoebel barriers.