  We introduce stochastic Discrete Laplacian Growth and consider its
deterministic continuous version. These are reminiscent respectively to
well-known Diffusion Limited Aggregation and Hele-Shaw free boundary problem
for the interface propagation. We study correlation between stability of
deterministic free-boundary problem and macroscopic fractal growth in the
corresponding discrete problem. It turns out that fractal growth in the
discrete problem is not influenced by stability of its deterministic version.
Using this fact one can easily provide a qualitative analytic description of
the Discrete Laplacian Growth.
