In the penultimate episode of Volume Three, the following developments affected various characters...
Claire: We're 16 years in the past and Claire and Hiro are still on the rooftop, witnessing Claire as a baby being given to her father. The older Claire decides to follow her younger version around and ensure that she is never implemented with the catalyst. Guess some people can't handle the responsibility. Eventually, Claire confronts HRG and basically tells him about the future. He says to love his baby and to not heed the company's catalyst call.
As will be discussed later, Claire is then sent forward again in time by Arthur Petrelli. Yes, this was an confusing to watch as it was to summarize.
Hiro: He's also still 16 years in the past. Hiro overhears his parents talking about where the catalyst ought to go, as his mother - who appears to have "the light" inside of her is about to die - and Hiro chooses to be brave. When his father is gone, he opens up to his mother. She sees that this older boy is her son and she cures his memory loss. She then puts the catalyst inside Hiro, just as she passes away.
Everything seems to be resolved (yeah, right), until Arthur shows up on the rooftop, takes Hiro's ability and the catalyst. He launches Hiro over the edge and he's left dangling by a flag pole. That all seemed rather easy for Arthur.
Parkman/Ando/Daphne: These three sprint to NYC and have the incredible good fortunate to track down the head of the bike messengers. He happens to have the last sketches of Isaac Mendez and when he shows then to this trio, they see the state Hiro is left in. But there's a silver lining, apparently: now that Arthur can complete the formula, maybe he can give someone else time traveling abilities and he/she can go back and save Hiro.
Ando gets inspired and wants to take on this ability. So the threesome is left trying to determine how to get to the formula (MAJOR story line issue here: if there is some good to the formula, as this trio determines, how can Arthur be pained as such an evil presence? It seems like his plan may not be so bad after all, right?).
Nathan: He arrives at Pinehearst and is ready to seize control. He talks with Marines that have volunteered to be injected with the formula in order to fight better. At the end of the episode, the first example that is injected the formula ends up throwing a chair through the glass, showcasing his super strength. We guess that's supposed to not bode well for humanity.
Sylar: After killing Elle, he truly returns to his former ways. Somehow, Sylar tracks down the location of a woman that can tell if someone is lying. He kills her, takes her power and heads over the Pinehearst. Once he arrives, he finds Peter and the Haitian - who has been tasked with murdering Arthur - and does the dirty work for them.
He stops Peter's bullet in mid-air, asks Arthur if he's really his father and now knows that he's lying when he says yes. Sylar therefore lets the bullet strike Arthur in the temple, taking him out for good.