You BASTARD. This is INCREDIBLY PROBABLE.
(And using "probable", I assure you, in the realm of One Piece theorizing and prediction formulating, is a damn compliment. Everyone here can probably attest to that.)
Seriously, as a devout One Piece fanatic, I think you've struck gold. Based on your compiled Oharan-esque research, I have to say: this is highly probable and congruent to all things One Piece.
Inherited Will.
I'm currently on my fifth or sixth go-around of the anime series, and I literally just concluded the Drum Island arc (pre-adventured naive Chopper is totes adorbs). This arc, as with all the wonderful, hilarious, exhilarating, heartwarming, tragic, deeply saddening, cool, awesome, hopeful, and INSPIRING tales Oda sings us, did not cease to fail in jolting my system with a cornucopia of utter, shivering AWE - the best stories affect you physically (it's tingly) - from the epic majesty and catharses these arcs bring. It got me to ponder the themes and meanings of the series that were first introduced and reinforced in this particular arc, relative to the chronology of how Oda meticulously peppers in clues of the bigger, GRANDER, mysteries still lying ahead as we follow his epic.
I'm a reader/viewer who gets more out of repeated viewings. This time, I was groovin' the vibe of Chopper's backstory and was caught much deeper this time around into its spell. Doctor Hiluluck was a fucking awesome character. Goofy and a quack, and really moving. In his final moments, he was joyous. He knew he was dying, but declared he won't die (remind you of someone?) because he won't be FORGOTTEN! His will, his DREAM, will live on! And it did! With a glorious smile stretched on his goofy face (remind you of certain peeps?), off he went, and from there, his final act gave the final push and inspired (/will-inherited) Dalton to resist against Wapol's stupid tyranny and inspired Dr. Krueha to carry on his dream of making sakura bloom in the winter island while also taking in Chopper to teach him how to become a kick-ass-first-class doctor (with Chopper inheriting his will as well). It got me really into thinking about that inherited will thing. It's been such a staple in the series, as with all the Strawhats' and their mentors and their dreams too.
Then, in the course of the series, this is where "The Will of D." is first introduced. Being as this is the first arc in which the theme of "inherited will" is outspokenly played out by a character in the telling, it's appropriate and significant. So what is The Will of D.? Well. I thought I was the first person to figure it out. At least a partial, concrete aspect of it. Total epiphany moment. Then right before posting about it, I googled that shit, and then stumbled onto this forum post for the first time.
And you sir, blew my fucking mind.
It all makes complete sense. Why the fuck WOULDN'T the greatest treasure in the world of One Piece be to bring the whole world into ONE PIECE? The loveliness of that fact is the gift of FREEDOM, and with that THE WHOLE WORLD. The entire planet would be completely accessible! Can you imagine THE ADVENTURE??? You can go anywhere and do anything! The greatest treasure is freedom; the greatest treasure is THE WORLD! Freedom is a pirate's greatest treasure!!!!
There's a moment in the Drum Island arc (or "Tony-kun's arc", teehee) that hit home to me about the wonders of being a pirate. There's a part where Jamaguchi is mouthing about being the king to a snowbird for some reason. "I am the King!" (Something he continuously brags throughout the arc, like some really obnoxious Tone Dial) And before HE TRIES TO EAT THE SNOWBIRD, our future Pirate King shuts him up:
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"Whether you're a king… Or whether you're a God... Who's great, who isn't great... It doesn't matter! Because I'm a pirate."
Dayummm. (the God part in the quote foreshadows a bit too, hmmm?)
What being a pirate truly means is being free to do whatever you want, whenever you want! With the only rule being: THERE ARE NO RULES, except giving proud allegiance to your own skull and cross bones! And that's FUCKING AWESOME!
So from witnessing Hiluluk's mention of not truly dying, that his will, his DREAM will be carried out after his "death", and going out smiling assured of that, I conceived my theory of "The Will of D.":
The Will of D. is exactly that: someone's inherited will. The most legendary one of them all. Most likely, there was a prominent figure during the time of the Ancient Kingdom, who aimed to do something incredible (cough cough, ahem). I'm tempted to refer to this prominent figure as "D." Because "D." just makes for a fucking cool name for a character. The Will of D., D.'s Will, it makes sense right? This man (it's gotta be a man, sorry ladies, this story IS about manliness) had a dream he wished to achieve but failed to do so. However, this dream, this will, was the greatest of them all, probably the dream of the whole Ancient Kingdom. Therefore it has become THE will. His legacy! Even after his tragic defeat against the powers that would become The World Government, his dream would continue on. I imagine when Oda reveals D.'s flashback, a man with a striking resemblance to Roger and Luffy, deathly bloodied from an awesome battle, proudly grins with a DON! to the whole world: "EVEN AFTER I'M GONE, MY DREAM WILL COME TRUE!!!!!!" Or something along those lines.
As Hiluluk said, a person only truly dies when they are forgotten. And the best way to keep his memory alive, his DREAM alive (other than, you know, etching giant unbreakable stone slabs scattered throughout the world), is by actually marking future generations' names. I believe the survivors from the Kingdom or D.'s actual descendants or whomever, gave the name "D." to their children and their children to their children to bestow The Will of D. to them. And these descendants all grew up to be foolhardy tenacious dreamers we all know, love, and admire in the world of One Piece.
In addition to that, I'm pretty confident now that the people who carry The Will of D. don't necessarily have to be blood related. Harking back to a quote from Whitebeard, it doesn't matter whether or not the bloodline dies, someone else will take up the will. And that's true with inherited will isn't it? Anyone can pick it up if they are inspired enough to do it, or worthy enough. Traditionally, the bestowing of "D." is familial and inherited through bloodlines, as it most likely is with The Monkeys and Jaguars. But someone else out of that bloodline who is deemed worthy enough (deemed by whomever authority, the actual person, the mysticism of One Piece, or God– Oda himself) can engrave D. into the center of their name and carry on D.'s Will. This totally justifies why Jaguar D. Saul says the name runs in his family, but he's a giant, making the tad improbable connection he might be a distant relative to humans such as Luffy or Roger (but of course you can't completely dismiss the possibility of giant-to-human freak-nastying). It also justifies how Gol D. Roger fell in love and had a child with a person named Portgas D. Rouge. (Do you think they're actually related to each other?Gross!) Finally, since the Will of D. isn't limited to blood-related family, isn't that much more lasting? Boundless? The surname is kept, but D. is actually just a middle name! Anyone can have it!
Well there you have it. That's my addition to the Will of D. theory. In terms of the will itself, it seems the carriers are all characteristically strong-willed, simple-minded, and fearless of death. Maybe it's just a coincidence, maybe the people who give them their names upon birth know they are capable whether through genetic inheritance or whatever. Regardless of how the D. becomes imprinted into the person's identity, the name certainly grants or classifies people with unworldly personality traits. Of course there are still lots of mysteries left and questions to be answered, but I think we're all making much better educated guesses with the material Oda's revealed to us so far. In all likelihood, Joy Boy is probably the origin of the Will of D. The name makes me think he was Luffy-esque and with the personality trait of a D. carrier.
Overall, that inherited will thing is starting to really sink in. Hiluluk's smiling visage upon his death was so proud and confident, like all of the Will of D. carriers upon their death. Just so certain their dream WILL come to fruition even after leaving the world of the living. That's deep, man. And with that confidence, it makes total sense that the Will of D. carriers have that air of fearlessness towards death. In the grand scheme of things, they accept the inevitability of death, and perhaps innately understand that their dreams WILL come true, just passed onto someone else. Maybe not necessarily their own dreams, but perhaps innately feeling that the Will of D. will continue until it is fulfilled. That confidence, that innate belief, must be so comforting. And you can tell that whoever has this overwhelming content are the ones who are also the most worthy to be a "Pirate King." Endlessly smiling. Pretty much in every portrayal we've seen of Roger, he was always smiling, wasn't he?
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…Who else do we know with a constant grin on his face?