  We investigate the problem of growing clusters, which is modeled by two
dimensional disks and three dimensional droplets. In this model we place a
number of seeds on random locations on a lattice with an initial occupation
probability, $p$. The seeds simultaneously grow with a constant velocity to
form clusters. When two or more clusters eventually touch each other they
immediately stop their growth. The probability that such a system will result
in a percolating cluster depends on the density of the initially distributed
seeds and the dimensionality of the system. For very low initial values of $p$
we find a power law behavior for several properties that we investigate, namely
for the size of the largest and second largest cluster, for the probability for
a site to belong to the finally formed spanning cluster, and for the mean
radius of the finally formed droplets. We report the values of the
corresponding scaling exponents. Finally, we show that for very low initial
concentration of seeds the final coverage takes a constant value which depends
on the system dimensionality.
