Edit: this refers to the Shaya post some posts back.
I'm not going to pretend to support the tri-split, but I can clear up some points.
With the splits we are talking about the one possible Child and two possible Adult splits. Link failing = he dies at some point on his adventure (guays, etc.), as a child or adult doesn't really matter as it all leads into Ganon taking over Hyrule and staying in control in the future. Then we obviously have the other two splits we always knew.
Ganondorf does get sentenced to death "as the story goes". The execution is shown as a flashback in TP. It is generally accepted as obvious that the successful Link sent back to childhood at the end of OOT revealed the "future" events to Zelda, and the royal family arrests him. In this timeline Ganon is not yet stuck in the Sacred/Twilight Realm until the execution goes wrong and the Sages seal him there as a last resort. Also shown in TP. Link (via bloodline) always holds Courage in this scenario, just as Ganon always holds Power: a product of the Triforce being distributed in OOT previous to Link being sent back and having Ganon sentenced. As a side note, you can actually see it on Link's hand in TP.
Courage is not lost in the A Link to the Past split; the Triforce actually is shown and acquired (all 3 parts) in ALTTP. Later games in this split also show (Oracles) or imply (Originals) that Link is in possession of at least one portion of the Triforce. As a side note, you might assume OOT Link fails as a child as the Triforce is still whole when you collect it in ALTTP. The reason Ganon is sealed and Hyrule is "semi-peaceful" in ALTTP is the Imprisoning War (clearly mentioned in ALTTP materials), though I'm not too sure how it fits. Previously in the 2-prong timeline it was accepted that OOT and its prologue ARE the Imprisoning War and ALTTP was a product of the Adult split (in 3-prong terms, the successful one). It does sound close though so I'm assuming Hyrule Historia does cover some kind of reasoning if this timeline actually is legit. Btw, there are 7 descendants including Zelda, not 8 (not important, just clarifying).
As you mentioned, TWW line needs little explanation. Link literally collects Courage during his adventure and Ganon is turned to stone at the end. No later games in that split feature Ganon in any manner.
more with edit:
But doesn't the ending of OoT after zelda sends link back show him leave the temple of time with the master sword pedestal? In other words, Ganondorf has already killed the king, caused problems, etc.
Link is sent back to before he meets Zelda in OOT. He IS shown returning the Master Sword though, but then again, Zelda time mechanics are never accurate to real time mechanics (just look at SS).
edit2:
some more clarifications based on new info, basically tri-split is real
http://www.newnintendo.net/blog/2011/12/22/hyrule-historia-timeline-details-spilled-branch/
http://www.newnintendo.net/blog/2011/12/22/hyrule-historia-timeline-visual-representation/
GlitterBerri is an older member of the Zelda community who has done many translations in the past, this translation is legit
- There is no Hero present for TWW because Link is sent back at the end of OOT.
- In the failure split Link dies directly to Ganon and Ganon obtains the whole Triforce.
- Imprisoning War = the Sages seal Ganon away with the whole Triforce when Link dies, hordes of villains rush to the Sacred Realm searching for the Triforce and eventually the Sacred Realm is overflooded with evil and turns into the Dark World.
Quicklink to updated timeline image with some reasonings:
http://www.newnintendo.net/wp-content/uploads/2011/12/timeline.jpg
For the record I think Link never existing is much more of a copout than Link actually dying in OOT.
And this timeline still has some blatant holes such as FS/FSA but I'm sure if they can explain away the Imprisoning War then they can explain away FSA not being a direct sequel to FS. More likely than not the implications in FSA about it being a direct sequel were a localisation error.