  In this paper we prove that the limit set of any Weil-Petersson geodesic ray
with uniquely ergodic ending lamination is a single point in the Thurston
compactification of Teichm\"uller space. On the other hand, we construct
examples of Weil-Petersson geodesics with minimal nonuniquely ergodic ending
laminations and limit set a circle in the Thurston compactification.
