Stochastic model in the Kardar-Parisi-Zhang universality class with minimal finite size effects

We introduce a solid-on-solid lattice model for growth with conditional evaporation. A measure of finite size effects is obtained by observing the time invariance of distribution of local height fluctuations. The model parameters are chosen so that the change in the distribution in time is minimum. On a one-dimensional substrate the results obtained from the model for the roughness exponent alpha from three different methods are same as predicted for the Kardar-Parisi-Zhang equation. One of the unique features of the model is that alpha as obtained from the structure factor S(k,t) for the one-dimensional substrate growth exactly matches the predicted value of 0.5 within statistical errors. The model can be defined in any dimensions. We have obtained results for this model on two- and three-dimensional substrates.