The way I see it there are four possible answers:
- They are hereditary
- Each piece goes to the one worthy of it
- Each piece goes to the one who most desires it
- Straight reincarnation
But none of these quite make sense. Below I have listed and pointed out the issues with each
In Wind Waker and Twilight Princess, it seems as if they had their pieces of the Triforce all along, almost as if it is hereditary, but this does not match with the fact that at the beginning of Wind Waker it specifically states that the world is in the condition that it's in because there was no Hero of Time, which is not possible if the Hero of Time is simply a descendant of the Hero of Time. Furthermore, because even though it has never been confirmed, one of the iterations Link and Zelda (Phantom Hourglass,Skyward Sword) probably got married and had kids, given that Link and Zelda are never related, they can't both be descended from those two.
While this explanation holds for Link and possibly for Zelda (she's never demonstrated doing anything particularly wise, in fact, it is her idea to open the Door of Time, allowing Ganondorf to get to the Triforce), few can say it fits Ganondorf, each variation is different, but they are all plot cunningly, and though they demonstrate patience, it does not show them worthy of supernatural power.
This one makes the most sense in Ganondorfs case, it says exactly that in game, and it could hold for Zelda (she never really states her desires, other than the world not ending). But Link is always kind of pulled from a blissful existence into the cruel world by extraordinary circumstances. Now you could say that he at this point desires courage ( to rescue his sister, to find Illia, to fulfill the Deku Tree's command) but it is implied he is the hero because he had the Triforce, not the other way around.
This is the most popular theory, and for a good reason, it is almost directly supported in Skyward Sword. Although this one holds up moderately well there are a few issues.
Ganondorf is always an incarnation of Demise and always greatly desires power. This holds fairly well across all games, Ganondorf is always powerful and desires more. The only issue I can think of is why is Ghirahim (his weapon) never reincarnated? Though Fi never appears again, it could be said that she remains as the spirit of the Master Sword, Ganondorf only wields a sword two other times that I know of, and they don't appear to have any special properties.
Link, as "The Chosen Hero" has the easiest criteria to fill for reincarnation, and for the most part, it fits. Although his actions and motivations for such actions change with each game,he is relatively the same from game to game. The difference is, sometimes he receives the Triforce of Courage (Skyward Sword) sometimes he has it from the beginning (Wind Waker, Ocarina of Time) sometimes its not entirely clear (Twilight Princess), and if he were reincarnated it would be expected to be the same.
Zelda is the one that really throws this theory though. From one game to another, everything about her changes, her appearance, her position in her family, the exact nature of her powers, and her emotions and actions towards Link. Most notably, her role in Ganondorf's/Demise's destruction changes drastically from one to another
- In Skyward Sword she does nothing, though it is her power that keeps him contained, once he is free she is helpless and Link is fighting to save her.
- In Ocarina of Time she acts as a channel for the power of the Sages to pin Ganon in order for you to finish him off
- In Wind Waker she gets a "kill assist" wielding the light arrows while you strike Ganondorf with your sword
- Most notably, she has almost no part to play in Twilight Princess
By the reincarnation theory, her part would be at least somewhat similar as Ganondorf and Link's are, not diametrically different and variable.
To sum up everything I just said, if the Triforce(s?) is/are not hereditary, how do they end up in the people they do? (Aside from "destiny")