  We study Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory of phase conversion in
finite volumes. For the conversion time we find the relationship $\tau_{\rm
con} = \tau_{\rm nu} [1+f_d(q)]$. Here $d$ is the space dimension, $\tau_{\rm
nu}$ the nucleation time in the volume $V$, and $f_d(q)$ a scaling function.
Its dimensionless argument is $q=\tau_{\rm ex}/ \tau_{\rm nu}$, where
$\tau_{\rm ex}$ is an expansion time, defined to be proportional to the
diameter of the volume divided by expansion speed. We calculate $f_d(q)$ in
one, two and three dimensions. The often considered limits of phase conversion
via either nucleation or spinodal decomposition are found to be volume-size
dependent concepts, governed by simple power laws for $f_d(q)$.
