Traps are unnecessary, high level rex babies are unnecessary, running away is unnecessary, I have tamed 3 cryofridges of these guys. What I do is kill a low level baby rex, I have a bunch bred up just for this now. Walk the dead baby rex up to the Carcharo, making sure that when the Carcharo turns to eat the dead baby rex that it will not be damagaed by the environment, keep holding onto the dead baby and let the Carcharo eat it (you have a 50-50 chance that it hits you a little too when it eats), mount the Carcharo and kill large, high level dinos (rexes, brontos, mammoths, diplos, rhinos, yutys, carnos, etc). On 3x a lvl 90 or lower takes one baby rex, over lvl 90 takes 2 baby rexes.

More Carcharodontosaurus Taming & KO Tips