We apply a recently developed analytic but approximate method to study surface and surface-induced capillary transitions in a solution of polydisperse linear and/or branched polymers confined between two infinite but identical surfaces. We use an equilibrium polymerization model where various densities in the system are controlled by the corresponding activities. The bulk region, i.e., the central region between the surfaces may or may not be in the bulk equilibrium state (see the text). We find a line of first-order transitions, commonly known as a prewetting transition line, passing through the phase separation point in the bulk equilibrium state, at which the surface undergoes a first-order transition. For a certain range around the bulk equilibrium transition point, the bulk region undergoes a stable-metastable transition. This presents us with the possibility of being able to prepare the system in a bulk metastable state, no matter how far apart the two surfaces are. This range is found to be identical to the range of metastability for the bulk equilibrium state. Outside of this range, the transition line behaves like a prewetting transition line and, as usual, terminates at surface critical points, one on each side of the above range.