  We prove that most quasi-distributions can be written in a form similar to
that of the de Broglie-Bohm distribution, except that ordinary products are
replaced by some suitable non-commutative star product. In doing so, we show
that the Hamilton-Jacobi trajectories and the concept of "classical pure state"
are common features to all phase space formulations of quantum mechanics.
Furthermore, these results provide an explicit quantization prescription for
classical distributions.
