  We study by first principle computer simulations the low temperature phase
diagram of bosonic dipolar gases in a bilayer geometry, as a function of the
two control parameters, i.e., the in-plane density and the interlayer distance.
We observe four distinct phases, namely paired and decoupled superfluids, as
well as a crystal of dimers and one consisting of two aligned crystalline
layers. A direct quantum phase transition from a dimer crystal to two
independent superfluids is observed in a relatively wide range of parameters.
No supersolid phase is predicted for this system.
