  We prove the existence of scattering states for the defocusing cubic
Gross-Pitaevskii (GP) hierarchy in ${\mathbb R}^3$. Moreover, we show that an
energy growth condition commonly used in the well-posedness theory of the GP
hierarchy is, in a specific sense, necessary. In fact, we prove that without
the latter, there exist initial data for the focusing cubic GP hierarchy for
which instantaneous blowup occurs.
