The elution chromatography of flexible polymer molecules flowing through a microporous particle media is described by a combination of the Casassa model of flow segregation and the Di Marzio-Rubin lattice method for calculating the partition function of confined polymers. This combination of models allows for the treatment of polymer-surface interactions so that polymer chromatography in the exclusion and adsorption regimes can be described within a unified framework. The compensation point where repulsive polymer-surface excluded volume forces and short-range polymer surface attractive forces counterbalance each other offers opportunities for separating complex molecules. For example, calculations for a diblock copolymer where one of the components is at the compensation point ("adsorption Theta point") indicate that only the remaining block influences the elution of the block copolymer as a whole. This theoretical result accords with experiments on block copolymers. This singular observation provides support for the Casassa viewpoint of molecular partitioning dominated polymer elution. The chromatography of triblock copolymers, stars, and combs is also examined to determine the selectivity of elution chromatography for separating these molecular architectures. The theoretical development in the present paper should lead to improved methods for the characterization of polymers with different molecular architectures. These developments also suggest new tools for studying polymer adsorption from dilute solution.