We present Monte Carlo lattice simulations of proliferation of cells on a surface in the situation when the cell-cell adhesion is relatively strong and the cells may form islands and/or flattened hemispheres. The model parameters were chosen to mimic proliferation of adult rat neural stem cells (or, more specifically, adult hippocampal progenitor cells) deposited on polyornithine and laminin coated polystyrene. The results obtained show that the spatial constraints on cell division may result in slowdown of the exponential growth. Depending on the rules used for cell division, this effect may be either nearly negligible or appreciable. In the latter case, the scale of the deviations from the exponential growth is comparable with that observed in our experiments. In the simulations, the slowdown of the growth starts however somewhat earlier and occurs in a less abrupt manner. This seems to indicate that the spatial constraints on division of cells are not the main factor behind the experimentally observed termination of the growth.