The goal of this paper is to show that the wetting behavior of simple fluids on a repulsive solid surface - especially the "drying" phenomenon - is closely related to the proximity of the supercritical state of the bulk fluids to their vapor-liquid coexistence region. We propose here a new DFT (the star-function based density functional theory, s-DFT) that is based on the functional Taylor expansion of the intrinsic free energy F[rho] and the singlet direct correlation C-w((1)) to arrive at closed-form expressions for both quantities without truncations or approximations. The two formulas are mutually consistent because of the introduction of a star function S-w that has been shown to be the functional primitive of the bridge function B-w, i.e. delta S-w*/delta rho = B-w (L.L Lee, J. Chem. Phys. 97(1992)8606[34]). The new formulation is applied to the Lennard-Jones molecules adsorbed on a planar hard wall (LJ/HW). We carried out new Monte Carlo simulations for this system. Since the s-DFT uses a bridge function B-w, we demonstrate (i) the existence of a set of data (inverted from the MC information) that can perform as the bridge function and reproduce accurately the density profiles rho((1))(w)(r); (ii) this set of data can be "fitted" by a function-form with acronym ZSEP; finally (iii) ZSEP expresses the bridge function B-w in terms of a new renormalized basis function gamma(H), i.e. B-w(gamma(H)). The existence of a bridge function dispels some of the misconceptions that the bridge-function based formulations did not describe the "drying" behavior. We also show that for the high density case ZSEP equation can qualify as a "closure relation", but seems to deteriorate for the two low-density supercritical states that are close to the bulk saturated liquid phase boundaries. (C) 2010 Elsevier B.V. All rights reserved.