I don't see how Tarver can be great in any estimation. He had a great win against Roy Jones, but not a great career.
I'd say he's borderline very good. Probably doesn't quite cross the threshold into very good for me though. It is arguable though.:good
Tarver was good for a short period of time - circa post-Harding1-Jones2. Good, slightly awkward puncher. Never a great fighter, of course. He became ordinary very quickly - Glen Johnson fights were nothing special at all.
To see him punched out and sprawling around the ring after throwing a total of 200 punches over 12 rounds in Jones III was a disgrace. I wish Jones wasn't totally shot and somehow found a way to put him out of his (and our) misery.
He had it at his fingertips but blew it. I had him beating Johnson both times and had he stayed motivated maybe he'd have fared better against Hopkins, Dawson and Woods. He had the right names around to reach a level of greatness, I'm convinced of that, he just didn't really have the right mix of talent and motivation after the Jones trilogy. Going up in weight for Rocky was a bad idea as was taking Hopkins so lightly. He was very good though and at his best he presents a tough nights work for anyone.
His run from Harding 1 up until Hopkins is an excellent one I think. Aside from the obvious Jones x3, you have Johnson x2, Harding, Griffin and Reggie J who had been 3 of Jones best challenges. He's basically fought the best in his division over that period and beat them all. The resume isn't that deep but some of those considered top15 LHWs don't have better LHW resumes. Greatness is subjective, but Tarver is a better LHW than say Maxim for instance. What people don't realise or forget is he was as old as Jones himself and he was 37 when he lost to Hopkins and 40 when he lost to Dawson. He was also likely drained against Hopkins after bulking upto 220lbs for the Rocky movie. BTW he won he every round against Clinton Woods and agree he beat Johnson both times