  The von Neumann algebra free product of arbitary finite dimensional von
Neumann algebras with respect to arbitrary faithful states, at least one of
which is not a trace, is found to be a type~III factor possibly direct sum a
finite dimensional algebra. The free product state on the type~III factor is
what we call an extremal almost periodic state, and has centralizer isomorphic
to $L(\freeF_\infty)$. This allows further classification the type~III factor
and provides another construction of full type~III$_1$ factors having arbitrary
$\Sd$~invariant of Connes. The free products considered in this paper are not
limited to free products of finite dimensional algebras, but can be of a quite
general form.
