  The Kolmogorov-Johnson-Mehl-Avrami model, which is a nucleation and growth
poissonian process in space, has been implemented by taking into account
spatial correlation among nuclei. This is achieved through a detailed study of
a system of distinguishable and correlated dots (nuclei). The probability that
no dots be in a region of the space has been evaluated in terms of correlation
functions. The theory has been applied to describe nucleation and growth in two
dimensions under constant nucleation rate, where correlation among nuclei
depends upon the size of the nucleus. We propose a simple formula for
describing the phase transition kinetics in the presence of correlation among
nuclei. The theory is applied to the constant nucleation rate process when
correlation depends upon the nucleus-birth time. It is shown that the random
sequential adsorption and Tobin process can be analyzed in the framework of the
simultaneous nucleation case, admitting a common rationale that is apart from
an appropriate re-scaling they represent the same process from the mathematical
point of view.
