  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 NASA's 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.
