Polymer systems in slab geometries are studied on the basis of the recently presented Gaussian ellipsoid model [F. Eurich and P. Maass, J. Chem. Phys. 114, 7655 (2001)]. The potential of the confining walls has an exponential shape. For homogeneous systems in thermodynamic equilibrium we discuss density, orientation, and deformation profiles of the polymers close to the walls. For strongly segregated mixtures of polymer components A and B equilibrium profiles are studied near a planar interface separating A and B rich regions. Spinodal decomposition processes of the mixtures in the presence of neutral walls show upon strong confinement an increase of the lateral size of A and B rich domains and a slowing down of the demixing kinetics. These findings are in agreement with predictions from time dependent Ginzburg-Landau theory. In the case, where one wall periodically favors one of the two mixture components over the other, different equilibrium structures emerge and lead to different kinetic pathways of spinodal decomposition processes in such systems.