We study the distributions of effective diameter ($D$), beaming parameter ($eta$), and visible geometric albedo ($p_V$) of asteroids in cometry orbits (ACOs) populations, derived from NASAs Wide-field Infrared Explorer (WISE) observations, and compare these with the same, independently determined properties of the comets. The near-Earth asteroid thermal model (NEATM) is used to compute the $D$, $p_V$ and $eta$. We obtained $D$ and $p_V$ for 49 ACOs in Jupiter family cometary orbits (JF-ACOs) and 16 ACOs in Halley-type orbits (Damocloids). We also obtained $eta$ for 45 of them. All but three JF-ACOs (95% of the sample) present a low albedo compatible with a cometary origin. The $p_V$ and $eta$ distributions of both ACO populations are very similar. For the entire sample of ACOs, the mean geometric albedo is $bar{p_V} = 0.05 pm 0.02$, ($bar{p_V} = 0.05 pm 0.01$ and $bar{p_V} =0.05 pm 0.02$ for JF-ACOs and Damocloids, respectively) compatible with a narrow albedo distribution similar to that of the Jupiter family comets (JFCs), with a $bar{p_V} sim 0.04$. The $bar{eta} =1.0 pm 0.2$. We find no correlations between $D$, $p_V$ , or $eta$. We compare the cumulative size distribution (CSD) of ACOs, Centaurs, and JFCs. Although the Centaur sample contains larger objects, the linear parts in their log-log plot of the CSDs presents a similar cumulative exponent ($beta = 1.85 pm 0.30$ and $1.76 pm 0.35$, respectively). The CSD for Damocloids presents a much shallower exponent $beta = 0.89 pm 0.17$. The CSD for JF-ACOs is shallower and shifted towards larger diameters with respect to the CSD of active JFCs, which suggests that the mantling process has a size dependency whereby large comets tend to reach an inactive stage faster than small ones. Finally, the population of JF-ACOs is comparable in number that of JFCs, although there are more tens-km JF-ACOs than JFCs.
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