The growth of a large crystal into a fine-grained polycrystal of the same phase is considered through a two-dimensional model. The macroscopic driving force for growth depends only on the average energy of the grain boundaries of the polycrystalline matrix. The analysis reveals a dependence of the local driving force and effective mobility on the orientation of the interface between the large crystal and the matrix. The orientations with very low energy relative to the neighboring orientations also have low effective mobility. Applications are found in modeling of abnormal grain growth in ceramics and in experiments designed to measure the mobility of grain boundaries.