  Hard-core dipolar bosons trapped in a parallel stack of N>=2 1D optical
lattices (tubes) can develop several phases made of composites of particles
from different tubes: superfluids, supercounterfluids and insulators as well as
mixtures of those. Bosonization analysis shows that these phases are
threshold-less with respect to the dipolar interaction, with the key "control
knob" being filling factors in each tube, provided the inter-tube tunneling is
suppressed. The effective ab-initio quantum Monte Carlo algorithm capturing
these phases is introduced and some results are presented.
