  We investigate the equilibrium phase-coherence properties of Bose-condensed
particle systems, focusing on their shape dependence and finite-size scaling
(FSS). We consider three-dimensional (3D) homogeneous systems confined to
anisotropic L x L x L_a boxes, below the BEC transition temperature $T_c$. We
show that the phase correlations develop peculiar anisotropic FSS for any
$T<T_c$, in the large-$L$ limit keeping the ratio \lambda = L_a/L^2 fixed. This
phenomenon is effectively described by the 3D spin-wave (SW) theory. Its
universality is confirmed by quantum Monte Carlo simulations of the 3D
Bose-Hubbard model in the BEC phase. The phase-coherence properties of very
elongated BEC systems, \lambda>>1, are characterized by a coherence length
\xi_a \sim A_t \rho_s/T where A_t is the transverse area and \rho_s is the
superfluid density.
