A novel simulation model for crystallization of polymer mono-layers is presented and compared with experiments on short PEO chains. We assume that crystallized chains can exist in states of different degrees of order. The resulting morphologies are nonequilibrium intermediate structures which can further relax on increasingly long time scales. The parameters of the model are the maximum stretching length of the chains M, the energy of the crystal-crystal interaction in terms of the Metropolis rate p(0) and the barrier for increasing the degree of chain order p(S). Since flatly adsorbed chains in a mono-layer must be oriented upright in order to crystallize, diffusion controlled growth patterns emerge which change their morphology depending on the model parameters. Different morphologies can be used to compare the model phase diagram with experiments. For large values of M, the interplay of the ordering barrier p(S) and the unbinding barrier p(0) controls the growth morphologies as well as internal structures such as the average stem length L. We find the variation of L with temperature in agreement with empirical relations proposed from experimental observations. When the free chains of the reservoir are exhausted, the edges of the crystal start to relax into energetically favored states which stabilize the growth patterns at long time scales. Such patterns are frequently observed in experiments. For high barrier factors the chains are poorly ordered and relax into a pronounced hole-rim morphology as observed experimentally at low temperatures. At higher temperatures secondary relaxation processes result in a destruction of the growth morphology into dropletlike structures having a higher degree of internal chain order. (C) 2000 American Institute of Physics. [S0021-9606(00)50409-7].