A computer simulation model was developed to investigate spherulitic growth in polymers of infinite and plate-limited volume as well as in fibre-reinforced polymer composite systems. Parameters like thermal nucleation rate and athermal nucleation density, plate distance, and fibre content were varied. The simulation crystallization process was evaluated following Avrami’s method in the case of infinite volume and by stepwise approximation by Avrami functions in the case of limited volume. In addition, the simulation method allows the visualization of the growing entities at any phase of crystallization. Therefore the geometry of growing entities can be easily compared with the corresponding crystallization exponent. A good agreement between the crystallization exponent and the growth geometry was found. Depending on nucleation mode, "infinite" systems yield Avrami exponents of 3 and 4. In plate-limited volume, a transcrystallization effect was observed in case of high athermal nucleation density on plate surface and large plate distances. This particular skin effect decreases the three-dimensional growth to a one-dimensional needle-shaped one. Small plate distance changes the spherical to a disk-like growth, resulting in crystallization exponents of 2 or 3, depending on nucleation mode. The crystallization behaviour of fibre-reinforced composite systems is more complex. Low fibre content or large fibre distance and high athermal nucleation density on the fibre surface induce the formation of trans-crystalline zones. The three-dimensional growth of the spheres at the beginning is restricted by their neighbours, so that their geometry changes to a pyramidical one. They grow with a front normal to the fibre surface and the crystallization exponent is shifted in between 2.0 and 2.6 depending on nucleation density. High fibre content leads to a growth along the triangular channels between three adjacent fibres; the corresponding exponent amounts to 1.6.