  Using large scale quantum Monte Carlo simulations of lattice bosonic models,
we precisely investigate the effect of weak Josephson tunneling between 2D
superfluid or superconducting layers. In the clean case, the
Kosterlitz-Thouless transition immediately turns into 3DXY, with phase
coherence and superflow in all spatial directions, and a strong enhancement of
the critical temperature. However, when disorder is present, rare regions
fluctuations can lead to an intermediate finite temperature phase --- the so
called sliding regime --- where only 2D superflow occurs within the layers
without any transverse superfluid coherence, while a true 3D Bose-Einstein
condensate exists. Critical properties of such an unconventional regime are
carefully investigated.
