We have studied the anchoring of the nematic liquid crystal 5CB (4 '-n-pentyl-4-cyanobiphenyl) as a function of the surface wettability, thickness of the liquid crystal layer, and temperature by measuring the birefringence of a hybrid aligned nematic cell where the nematic material was confined between octadecyltriethoxysilane-treated glass surfaces, with one surface linearly varying in its hydrophobicity. A homeotropic-to-tilted anchoring transition was observed as a function of the lateral distance along the hydrophobicity gradient, typically in a region corresponding to a water contact angle of similar to 64 degrees. The effect of the nematic layer thickness was measured simultaneously by preparing a wedge cell where the thickness varied along the direction perpendicular to the wettability. The detailed behavior of the onset of birefringence was found to be consistent with a dual-easy-axis model that predicts a discontinuous anchoring transition from homeotropic to planar. The anchoring was independent of temperature, except within 1 degrees C of the nematic-to-isotropic transition temperature (T-NI). As the temperature approached T-NI, the tendency for planar anchoring gradually increased relative to that for homeotropic anchoring.