  Based upon first-principles methods, we investigate the magnetic anisotropy
and the spin-texture of Co adatoms embedded in the topmost Se network of the
topological insulator Bi$_2$Se$_3$ surface. We find the formation of
energetically stable magnetic moment perpendicular to the surface plane, S$_z$.
Our results for the pristine Bi$_2$Se$_3$ surface indicate the presence of
helical spin-texture not only in the massless surface Dirac states, but also
surface states resonant within the valence band present spin-texture. On the
other hand, upon the presence of Co adatoms we find that the out-of-plane
surface magnetism represents the dominant spin state (S$_z$), while the planar
spin components, S$_x$ and S$_y$, are almost suppressed.
