Synthesis of nanostructures of uniform size is fundamental because the size distribution directly affects their physical properties. We present experimental data demonstrating a narrowing effect on the length distribution of Ge nanowires synthesized by the Au-catalyzed molecular beam epitaxy on Si substrates. A theoretical model is developed that is capable of describing this puzzling behavior. It is demonstrated that the direction of the diffusion flux of sidewall adatoms is size dependent and has a major effect on the growth rate of differently sized nanowires. We also show that there exists a fundamental limitation on <?format ?>the maximum nanowire length that can be achieved by molecular beam epitaxy where the direction of the beam is close to the growth axis.