  We study the equations of black strings in spacetimes of arbitrary dimensions
with a negative cosmological constant and construct numerically non uniform
black strings solutions. Our results suggest the existence of a localised black
hole in asymptotically locally $AdS$ spacetime. We also present evidences for a
dependence of the critical dimension on the horizon radius.The critical
dimension represents the dimension where the order of the phase transition
between uniform and non uniform black string changes. Finally, we argue that
both, the regular asymptotically locally $AdS$ solution and $AdS$ black string
solutions with a very small horizon radius, present a negative tension. This
turns out to be an unexpected feature of the solutions.
