Did Frodo complete his quest?

[Nar]

You're right, Kalimac, but there is one other thing Frodo did: holding the power of the Ring, he told Gollum he would be cast into the fire himself if he ever touched Frodo again. Was he foretelling Gollum's future? Or was he inadvertently imposing a command on Gollum, using the ring's absolute power over him? If it's the second case, Frodo is directly (if unconsciously) responsible for destroying Gollum and thus the ring. Remember, he told Gollum earlier that if he had to, he would command Gollum to jump into the fire. I think ultimately, as you've said, it was a divine push that depended on the heroic efforts of Frodo and Sam to set things up. However, I think the divine push used, and depended upon, both Frodo's insight into Fate and the power of command the ring had imposed upon him, just as much as it depended upon Gollum's shaky footing and Sauron's carelessness in not installing that safety rail. (Who has time for home improvements when you're putting your neighbors to fire and sword? At least he kept his driveways paved.)

In other words, Frodo's words to Gollum on Mount Doom were both a foretelling and a command, which Frodo only half understood at the time. However, I think Frodo's spiritual self, on the other side, (the white robed figure with the wheel of fire) fully understood and intended all of it. This side of Frodo was highly developed by then, having withstood the Ring, and was fully capable of understanding the endgame as a consequence of all the players together, as well as the pattern that their play had imposed on the board.