We report on ab initio calculations of Pt(111) B-type step-edges decorated with Co chains of different thickness. As found experimentally, these Co n-wires show for n=1 (monowire) a large magnetic anisotropy that decreases for larger n in a non-monotonous way. Also the easy axis shows a oscillatory behavior with increasing n that can be traced back to competing effects arising from different strands of the thicker wires.