First of all, Carmine Persico was not on the lam from 1981-mid '80s. He was arrested in 1981, served a couple years in prison and was out of jail just in time for his next indictment. He only served a few months on the run before Fred DeChristopher gave him up.

Second, don't buy into anything that says the Persicos don't have any power anymore. There is no evidence whatsoever to support that. The last known acting boss was Andrew Russo, Carmine's first cousin who has been nothing but loyal to the Persicos since the 1970s. Before him was Ralph DeLeo, who had a panel under him helping run things. DeLeo was only brought into the family through Little Allie Boy, whom he met in prison. And although we don't know all the members of the panel beneath him, we know that Theodore Persico Jr. was, and we also know that Teddy Jr. was being groomed to take the reigns. We also know that, in the last known (aborted) making ceremony, the Persico influence was still strong even in the younger generations. You had Angelo Spata, the son-in-law of Carmine. You had Francis Guerra, Little Allie Boy's close friend in the 1990s. And you had Ilario Sessa, a staunch Persico loyalist during the war who was shot at by Orena rebels.
So, in short, all the evidence at hand points to the fact that the Persico brood is still firmly in charge. I know it's interesting to suggest that there are other forces at play, but just look at the evidence. Unless some enormous leadership shakeup happened from 2011 to today, the Persicos are still in charge, and they still have significant allies and sway on the streets.