  We study the most general contributions due to scalar field perturbations,
vector field perturbations, and anisotropic expansion to the generation of
statistical anisotropy in the primordial curvature perturbation \zeta. Such a
study is done using the \delta N formalism where only linear terms are
considered. Here, we consider two specific cases that lead to determine the
power spectrum P_\zeta(k) of the primordial curvature perturbation. In the
first one, we consider the possibility that the n-point correlators of the
field perturbations in real space are invariant under rotations in space
(statistical isotropy); as a result, we obtain as many levels of statistical
anisotropy as vector fields present and, therefore, several preferred
directions. The second possibility arises when we consider anisotropic
expansion, which leads us to obtain I+a additional contributions to the
generation of statistical anisotropy of \zeta compared with the former case,
being I and a the number of scalar and vector fields involved respectively.
