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The Asteroid Belt and the Kuiper Belt are relics from the formation of oursolar system. Understanding the size and spin distribution of the two belts iscrucial for a deeper understanding of the formation of our solar system and thedynamical process that govern it. In this paper, we investigate the effect ofcollisions on the evolution of the spin distribution of asteroids and KBO's.  We find that the power law nature of the impactors' size distribution leadsto a L\'evy distribution of the spin rates. This results in a power law tail ofthe spin distribution, in stark contrast to the usually quoted Maxwelliandistribution. We show that for bodies larger than 10 km, collisions alone leadto spin rates peaking at 0.15-0.5 revolutions per day. Comparing that to theobserved spin rates of large asteroids ($R>50$ km), we find that the spins oflarge asteroids, peaking at $\sim1-2$ revolutions per day, are dominated by aprimordial component that reflects the formation mechanism of the asteroids.Similarly, the Kuiper Belt has undergone virtually no collisional spinevolution, assuming current day density. Collisions contribute a spin rate of$\sim0.01$ revolutions per day, thus the observed fast spin rates of KBOs arealso primordial in nature.

Spins of large asteroids: Hint on a primordial distribution of their spin rates