WW's the best example, and I believe the SW also describes Ganon gained the ToX's power when he touched it.Judging by most Zelda games, I believe that the Triforce is something that the goddesses bestow upon someone. I can't remember a Zelda game where just touching the Triforce granted one its power.
WW Ganondorf is definately the same as OoT Ganondorf, and he also had the ToP from when he was sealed in OoT until the end of WW.
TP Link could have inherited the ToC whether he's HoT's descendent or not. It may have just picked him because he had the same heroic traits as HoT. The reason he didn't have to look for it while HoW did is the same reason Ganondorf got the ToP in TP.
I think one of three things happened:
1. The state of the Triforce is consistent along a line perpendicular to the flow of time, meaning when it splits in OoT's AT it also splits in the CT at the same time.
2. When Link went back in time after defeating Ganondorf in OoT, the ToX saw that he had received the ToC, and 'glitched' itself into thinking that the ToW and ToP must also be distributed.
3. Zelda went to 'check' on the ToX after Link told her about the AT, and she touched it. (Though I don't know how she'd get the ToW after doing a stupid thing like that.)