Possible phases in a semi-infinite nematic liquid crystal under condition of weak homeotropic anchoring are discussed. I present a theoretical investigation of the temperature and magnetic field dependence of paranematic (very weakly nematic ordering) wetting layers close to an aligning substrate. My investigation is based on Landau-de Gennes theory supplement by Nobili-Durand surface free energy. I find that a narrow temperature interval below the nematic-paranematic phase transition temperature which corresponds to paranematic boundary layer. The interval length depends on preferred order parameter at the surface and anchoring.