The processes of the nucleation, growth and liquid-like coalescence of
new phase islands (resulting from their lateral growth) are studied.
Analytical expressions are obtained for the cluster-size distribution
function and its moments, using the simplest laws of cluster growth. T
he pairwise coalscence process is shown to give rise to a number of ef
fects, such as Ostwald ripening, secondary nucleation and self-similar
ity of the size distribution function.