  In this paper, we classify the three-dimensional contact partially hyperbolic
diffeomorphisms whose stable, unstable and central distributions are smooth,
and whose non-wandering set equals the whole manifold. We prove that up to a
finite quotient or a finite power, they are smoothly conjugated either to the
time-one map of an algebraic contact-Anosov flow, or to an affine partially
hyperbolic automorphism of a nil-manifold. The rigid geometric structure
induced by the three invariant distributions plays a fundamental role in the
proof.
