[en] The kinetics of grain growth in nanocrystalline two-dimensional polycrystals and thin films can be controlled by the triple junctions of the microstructure. In the present work the influence of energy and mobility of grain boundaries and their junctions on annealing is investigated by analytic theories and modified Monte Carlo Potts model simulations. To that aim each structural feature of a polygonal grain is assigned its own specific energy and finite mobility, which results in four different limiting cases of self-similar growth kinetics each characterized by its own metrical and topological properties. (paper)