Description: There is a group of newly recognized asteroids in the main belt that are exhibiting cometary characteristics. We will call them Asteroidal Belt Comets or ABCs for short. The surprising property of these objects is that their orbits are entirely asteroidal while their behaviour is entirely cometary, with Tisserand invariants larger than 3.0, while all Jupiter family comets have Tisserand invariants smaller than 3.0. An analysis of their orbital and physical properties has resulted in the following conclusion. (1) We define the ‘detached group (DG)’ as those objects that exhibit cometary characteristics (sublimating water) and have aphelion distances Q  〈 4.5 au. The DG contains all the ABCs traditionally recognized, plus a few other members not traditionally recognized like 2P and 107P. With the above definition there are 11 members of the ABC group: 2P, 107P, 133P, 176P, 233P, 238P, C/2008 R1, C/2010 R2, 2011 CR42, 3200 and 300163 = 2006 VW139. And there are three members of the collisioned asteroids, CA, P/2010 A2, 596 Scheila and P/2012 F5 Gibbs. (2) In the literature a common reason for activity is interplanetary collisions. Active objects sublimate ices except for the CA that have exhibited dust tails due to collisions and 3200 Phaethon activated by solar wind sputtering. In this work, we will trace the origin of activity to a diminution of their perihelion distances, a hypothesis that has not been previously explored in the literature. (3) We have calibrated the blackbody (colour) temperature of comets versus perihelion distance, R , regardless of class. We find T  = 325 ± 5 K/ R . (4) Using a mathematical model of the thermal wave we calculate the thickness of the crust or dust layer on comet nuclei. We find a thickness of 2.0 ± 0.5 m for comet 107P, 4.7 ± 1.2 m for comet 133P and 1.9 ± 0.5 m for a sample of nine comets. Note the small errors. (5) We have located three ABCs in an evolutionary diagram of Remaining Revolutions (RR) versus Water-Budget Age (WB-AGE). ABCs lie together in the upper-right-hand corner of the diagram, as expected from physical arguments. (6) The RR versus WB-AGE diagram also defines the region of the graveyard of comets , as those objects with 1000 cy 〈 WB-AGE, where cy stands for comet years . Five members belong to the graveyard, 107P, 133P, 2006 VW139, D/1891 W1 Blanpain and 3200 Phaeton. Thus, we propose that the asteroidal belt contains an enormous graveyard of ancient dormant and extinct rocky comets, that turn on (are rejuvenated), in response to a diminution of their perihelion distance, caused by planetary perturbations.