Heart.

Just like its name, the "Heart" is a crucial item which the Order and the Earl had been looking for. It is the core of Innocence, where all Innocence originated. There should be one and only Heart.

The Conformer of the Heart has yet to be confirmed. At first, Komui analyzed that as the Heart was something powerful, then the Generals—who were likely to be stronger than the other exorcists—would have the highest possibility of being the conformer of the Heart. However, the Order recently found two new candidates who might have the chance of being the possessor of the Heart—and both of them are surprisingly young: Allen Walker and Lenalee Lee.

Both Allen and Lenalee possessed an Innocence which acted out of habit. Either of their Innocence had evolved. In Allen's case, his Innocence had been destroyed once however it took a completely new form after sometime. Meanwhile, after the fight with Eshi, Lenalee's Dark Boots turned into protective crystals surrounding her unconscious body, until she finally came to. It happened one more time when the Earl appeared right before the exorcists. The only difference that time was that Lenalee was awake inside the crystal. Even the Earl himself noticed her Innocence and attempted to attack her.

Both cases are strange because normally, Innocence does not act without the possessor's will. If you're saying that this was baseless conjecture because "only Allen had his Innocence destroyed" or "Lenalee was the only exorcist who was about to die". Why? Because even before the finding-Generals mission started, the Noahs had successfully destroyed some Innocence and killed their respective Accomodators. However, none of them, not even the Innocence, survived. Furthermore, inside the Ark, Kanda and Krory had also fought the Noahs to the verge of dying—or maybe they had actually died back then. However, there were no mentions of their Innocence saving them. Kanda's Innocence, Mugen, was in a bad shape, and the Science section had to work on it later on. When it was fixed, it didn't evolve. Lenalee's Dark Boots didn't get to be fixed, instead, it returned to be protected by Hevlaska because her synchronization rate was very low. However, it just evolved itself the next time she tried to synchronize.

This anomaly had made Allen and Lenalee's Innocence excluded from being ordinary weapons, and people had started to think of the possibility for either of those two being the possessor of the Heart.

the innocence's demolition

The only way to identify whether an Innocence is the Heart or not, probably, is to destroy the Innocence itself. If every other existing Innocence suddenly perished itself when a certain Innocence was destroyed, then that Innocence would be the Heart, without a doubt. However, this is obviously the NOT wisest step to do, because if Innocence extincts = no more weapons to fight Akumas = the Earl will conquer the world... or more like, wipe humans out.

Allen's Innocence was crushed by Tyki Mikk, once. Suman's Innocence didn't vanish when Allen's was destroyed, so we jumped to the conclusion that Allen's Innocence was not the Heart. Then why, anomaly aside, would his Innocence have a chance of being the Heart, after it was destroyed? Well, if Allen's Innocence really was the Heart, then I guess this would be the explanation: the Innocence that Tyki crushed back then was unstable. Simply put, it couldn't be a real Heart until it evolved and became more stable. It is possible that the Heart hides itself until it decides that the time has come. Who knows what will happen if Tyki once again try to destroy Allen's Crowned Clown?

On the other hand, Lenalee's Innocence was never destroyed. Well, after their encounter with the Earl which turned Lenalee's Dark Boots into crystals (as mentioned above), Tyki once tried to (by using Tease), however Allen reacted fast and killed the Tease before it reached Lenalee. We had no idea what would happen if the Tease managed to kill her. Well, if you didn't believe in my "unstable" argument above, then you could say that Lenalee got more chance of being the possessor of the Heart, compared to Allen.

Regarding the Dark Boots' evolution into what Komui called Crystallization type, he mentioned that other exorcists could probably have their Innocence evolve to a certain level, as well. However, nothing like that had happened as far as the story goes, leaving Lenalee's Innocence the only "exception" next to Allen's.

what i like to believe

As for my own opinion... I didn't want to believe the theory that either Allen or Lenalee possessed the Heart. Maybe it would be kind of boring, especially if it was Allen, since he was the main character of the series. If it was Lavi or Kanda, or any other exorcists, it would be interesting and totally unexpected for the fans, and would probably be a nice touch. Aside from that, my thoughts are leading to.. the validity of the theory. :| Because it would make more sense (compared to, for example, what I mentioned about Kanda above) especially if it was for the main character.

My other theory is, if the name "Heart" referred to one's heart, minds, feelings, or emotions, then it would fit those two even more. The evolution of their Innocence, can be seen as a reaction to the strong will and resolve of their hearts. Allen's heart had became more stable, and he made a resolve that his existence was to protect (or save, to be precise) both humans and akuma, because he loved them both. The same goes to Lenalee. Before, she still wished that all her fights and things like Innocence and Millenium Earl were just a dream. However, she finally became determined and wished for a strength that could protect her brother and everyone. Her Innocence reacted to her resolve, and began to synchronize with her even stronger than before.

Having said that, I think I'll go with the theory of Allen or Lenalee becoming the possessor of the Heart. I can't say who has the higher possibility. It might be Lenalee (because of Allen's interruption when a Tease tried to touch her), but it might be Allen (the main character, yes, and the 14th = even more complication). Or it could be someone totally unexpected, as well. I don't even know how the Heart will reveal itself as the Heart in the end, because I don't believe that all the Innocence will be destroyed. It probably has a nature that no one can tell as of now, that will rise to the surface and make everyone knows about the truth. Again, all we can do is just to wait and see.