  We study a single, motionless three-dimensional droplet growing by adsorption
of diffusing monomers on a 2D substrate. The diffusing monomers are adsorbed at
the aggregate perimeter of the droplet with different boundary conditions.
Models with both an adsorption boundary condition and a radiation boundary
condition, as well as a phenomenological model, are considered and solved in a
quasistatic approximation. The latter two models allow particle detachment. In
the short time limit, the droplet radius grows as a power of the time with
exponents of 1/4, 1/2 and 3/4 for the models with adsorption, radiation and
phenomenological boundary conditions, respectively. In the long time limit a
universal growth rate as $[t/\ln(t)]^{1/3}$ is observed for the radius of the
droplet for all models independent of the boundary conditions. This asymptotic
behaviour was obtained by Krapivsky \cite{krapquasi} where a similarity
variable approach was used to treat the growth of a droplet with an adsorption
boundary condition based on a quasistatic approximation. Another boundary
condition with a constant flux of monomers at the aggregate perimeter is also
examined. The results exhibit a power law growth rate with an exponent of 1/3
for all times.
