The combination of advection and migration of grain boundaries is analyzed on the basis of a simple mesoscale model, where parallelepipedic grains are considered under uniaxial compression straining. Strain hardening and dynamic recovery are described by the classical Yoshie-Laasraoui-Jonas equation. Grain-boundary migration is driven by the difference in dislocation densities between one representative grain and the average over the material. Finally, nucleation is assumed to occur at grain boundaries. Special attention is paid to the aspect ratio, which starts from unity (infinitely small cubic nucleus) and tends to zero when the grain disappears. In spite of the role of migration, the average shape of the grains is determined as a first approximation by their lifetimes.