We show that the anchoring memory of liquid crystals on solid substrates ca
n be completely removed by grafting highly mobile polymer chains. Using gra
fted polystyrene, we obtain uniform, stable, and reproducible memory-free a
nd conically degenerated anchoring of the nematic 5CB. The symmetry of the
conic anchoring enables two different zenithal anchoring breakings, towards
homeotropic and planar states. Under external torques we observe both of t
hem, with weak thresholds.