This paper discusses the modification of several spreading properties of a liquid on a solid surface by the addition of end-adsorbing polymers. End-adsorption of the polymers at the liquid-solid interface decreases the interfacial free energy. If this decrease is sufficient to overcome the negative spreading power of an otherwise nonspreading liquid, the liquid will spread on the surface. Using a self-consistent field method, we construct a phase diagram for spreading of a liquid drop of fixed volume as a function of the concentration of end-adsorbing polymers and the energy of end-adsorption to the surface. The equilibrium thickness of a spread film is also calculated and is shown to be closely related to the thickness of a self-assembled polymer brush in an unbounded fluid but relatively insensitive to the bare spreading power of the liquid or the Hamaker constant, which determine the equilibrium thickness of a film of a simple liquid. When a solid surface of a given area is covered by a film thicker than the predicted equilibrium thickness of a spread film, an instability due to the depletion attraction causes the excess liquid to form drops on top of the spread film of the equilibrium thickness.