  A simple, discrete, parametric model is proposed to describe conditional
(correlated) deposition of particles on a surface and formation of a connecting
(percolating) cluster. The surface changes spontaneously its properties (phase
transition) when a percolating cluster appears. The parameter k is included in
the probability p(k) of particles to stick together and form a cluster on the
surface. The case k=1 corresponds to the ordinary 2D percolation on a square
lattice. Thus the percolation threshold is controlled by the k-value: the
larger k the higher threshold for percolation. The growth model seen from the
percolation point of view allows us to describe several interesting
applications in addition to irreversible aggregation in the presence of a
repulsive force, k>1. For example, the occupied lattice sites might represent
regions of specific magnetization in an otherwise disordered medium. Then the
whole system is ordered or not according to the concentration of the deposited
particles. Object-oriented code is developed for the Monte Carlo part of the
calculations.
