Cellular automata simulation of recrystallization in two dimensions is carried out. The simulated microstrutural evolution is compared in detail with the predictions from mathematically exact analytical theories considering both kinetic and geometrical aspects. Very good agreement is observed between the cellular automata simulation and the theoretical results. Moreover, the simulated data is used to test new expressions recently derived to describe the evolution of the interfaces between recrystallized grains. This work focuses on recrystallization but its results are applicable to any nucleation and growth transformation.