  The existence of nonlinear objects of the vortex type in two-dimensional
magnetic systems presents itself as one of the most promising candidates for
the construction of nanodevices, useful for storing data, and for the
construction of reading and writing magnetic heads. The vortex appears as the
ground state of a magnetic nanodisk whose magnetic moments interact via
dipole-dipole potential?. In this work it is investigated the conditions for
the formation of vortices in nanodisks in triangular, square, and hexagonal
lattices as a function of the size of the lattice and of the strength of the
dipole interaction D. Our results show that there is a "transition" line
separating the vortex state from a capacitor like state. This line has a finite
size scaling form depending on the size, L, of the system as Dc=D0
+1/A(?1+B*L^2)?. This behavior is obeyed by the three types of lattices. Inside
the vortex phase it is possible to identify two types of vortices separated by
a constant, D=Dc, line: An in-plane and an out-of-plane vortex. We observed
that the out-of-plane phase does not appear for the triangular lattice. In a
two layer system the extra layer of dipoles works as an effective out-of-plane
anisotropy inducing a large S^z component at the center of the vortex. Also, we
analyzed the mechanism for switching the out-of-plane vortex component.
Contrary to some reported results, we found evidences that the mechanism is not
a creation-annihilation vortex anti-vortex process.
