  We give a complete study of the asymptotic behavior of a simple model of
alignment of unit vectors, both at the level of particles , which corresponds
to a system of coupled differential equations, and at the continuum level,
under the form of an aggregation equation on the sphere. We prove unconditional
convergence towards an aligned asymptotic state. In the cases of the
differential system and of symmetric initial data for the partial differential
equation, we provide precise rates of convergence.
