  Most states in the Hilbert space are maximally entangled. This fact has
proven useful to investigate - among other things - the foundations of
statistical mechanics. Unfortunately, most states in the Hilbert space of a
quantum many body system are not physically accessible. We define physical
ensembles of states by acting on random factorized states by a circuit of
length k of random and independent unitaries with local support. We study the
typicality of entanglement by means of the purity of the reduced state. We find
that for a time k=O(1) the typical purity obeys the area law. Thus, the upper
bounds for area law are actually saturated {\em in average}, with a variance
that goes to zero for large systems. Similarly, we prove that by means of local
evolution a subsystem of linear dimensions $L$ is typically entangled with a
volume law when the time scales with the size of the subsystem. Moreover, we
show that for large values of k the reduced state becomes very close to the
completely mixed state.
