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Even though it's been said before, the break down is pretty much this:
If you have ranged auto-attacks the items treat you as having ranged auto-attacks. If you have melee auto-attacks the items treat you as having melee auto-attacks. The same can be said for Youmuu's Ghostblade's active, or the slows applied by Phage, Triforce, Frozen Mallet, or Lizard Buff.
The only parts of Hurricane, Tiamat, and Hydra that are based on attack range is the splash damage/multi-target effect and, for Tiamat and Hydra, the active. So you still get attack speed, damage, life steal, and regeneration regardless of what your attack range is, which is handy if you pick them up on Elise, Kayle, Jayce, or Nidalee. As your attacks are never melee and ranged at the same time, you only use one of the AoE effects at a time (unless you shift to melee when ranged bolts are flying). Beyond that all melee champions with abilities masquerading as auto-attacks apply Hydra and Tiamat Splash on them (things like Twin Bite, Parrrley, and Blade Waltz) and no abilities masquerading as auto-attacks on ranged champions apply anything (things like Mystic Shot and Double-Up). You only get hurricane bolts on auto-attacks.
Originally Posted by Arcane Azmadi
There is only one ranged attack in the game that procs Tiamat/Hydra and that's Gangplank's Parrrley because it is specifically coded as a melee attack. Incidentally, that also means it will not proc the Hurricane even though it is ranged.
Hurricane bolts don't proc on anything but auto-attacks, if you use abilities masquerading as auto-attacks such as Double-Up or Mystic Shot you don't get the extra bolts.
I'm fairly certain the coding for Hydra and Hurricane has more to do with the champion being flagged as melee or ranged at the time as well, and Gangplank is melee 100% of the time in that regard.