  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 (KPZ) equation. One of the unique feature of the
model is that the $\alpha$ as obtained from the structure factor $S(k,t)$ for
the one dimensional substrate growth exactly matches with 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 a 2 and 3 dimensional substrates.
