  We consider the ground state properties of a trapped dipolar condensate under
the influence of quantum fluctuations. We show that this system can undergo a
phase transition from a low density condensate state to a high density droplet
state, which is stabilized by quantum fluctuations. The energetically favored
state depends on the geometry of the confining potential, the number of atoms
and the two-body interactions. We develop a simple variational ansatz and
validate it against full numerical solutions. We produce a phase diagram for
the system and present results relevant to current experiments with dysprosium
and erbium condensates.
