  We numerically analyze the dynamical generation of quantum entanglement in a
system of 2 interacting particles, started in a coherent separable state, for
decreasing values of $\hbar$. As $\hbar\to 0$ the entanglement entropy,
computed at any finite time, converges to a finite nonzero value. The limit law
that rules the time dependence of entropy is well reproduced by purely
classical computations. Its general features may then be explained by simple
classical arguments, which expose the different ways entanglement is generated
in systems which are classically chaotic or regular.
