Aims.In this work we study the cumulative size distribution of the population of asteroids in cometary orbits (ACOs), aiming to discriminate its cometary or asteroidal origin. Methods: .The cumulative luminosity function was determined based on the absolute magnitudes of the ACOs. The cumulative size distribution was then derived and compared to that of possible sources of ACOs, such as the Trojans and Hilda asteroids and Jupiter family comets. The size distribution of the two sub-populations, NEOs and non-NEOs, identified by Licandro et al. (2005) were also analyzed. Results: .The derived cumulative size distribution index of the ACO population is 2.55±0.04. The two subpopulations have distinct indexes: -2.20±0.04 and -2.45±0.04 for the NEOs and non-NEOs, respectively. The first value is similar to that of the Trojans and Hilda asteroids and the second to the Jupiter family comets. The obtained values suggest that the non-NEO sub-population of ACOs can be composed of a significant fraction of dormant Jupiter family comets. On the other hand, the NEO sub-population is mostly formed by scattered objects from diverse sources, including main belt asteroids.