  We obtain results on the unitary equivalence of weak contractions of class
$C_0$ to their Jordan models under an assumption on their commutants. In
particular, our work addresses the case of arbitrary finite multiplicity. The
main tool is the theory of boundary representations due to Arveson. We also
generalize and improve previously known results concerning unitary equivalence
and similarity to Jordan models when the minimal function is a Blaschke
product.
