  We study the formation of Majorana states in quasi-1D and 2D square lattices
with open boundary conditions, with general anisotropic Rashba coupling, in the
presence of an applied Zeeman field and in the proximity of a superconductor.
For systems in which the length of the system is very large (quasi-1D) we
calculate analytically the exact topological invariant, and we find a rich
phase diagram which is strongly dependent on the width of the system. We
compare our results with previous results based on a few-band approximation. We
also investigate numerically open 2D systems of finite length in both
directions. We use the recently introduced generalized Majorana polarization,
which can locally evaluate the Majorana character of a given state. We find
that the formation of Majoranas depends strongly on the geometry of the system
and if the length and the width are comparable no Majorana states can form,
however, one can show the formation of "quasi-Majorana" states that have a
local Majorana character, but no global Majorana symmetry.
