The monk class feature Unarmored Movement says:
At 9th level, you gain the ability to move along vertical surfaces and across liquids on your turn without falling during the move.
I am looking for an answer based in the rules as written, although interpretations and opinions are welcome.
I assert the rules support a notion of turns as meta-constructs useful for examining the game world at intervals, as opposed to a game world law of nature. As an example, if a character jumps and "runs out" of jump at the end of their turn while still jumping, I view the character as ending their round in mid-air, and that the jump gets continued on the character's next turn. I don't actually have rules citations to support my assertion, unfortunately.
This is important because I think it affects how far the monk can move along vertical or liquid surfaces. I don't know how, though.
As an example, let's assume a monk with 30' movement is 10' away from a 30' wide body of water. The monk moves 10' on land and then 20' on water and then the monk's turn is over. Does the monk fall in the water?
A slightly different example. Let's assume the monk has 30' of movement and is at the edge of a 1000' wide body of water. How far can the monk move before falling in?
One answer might be the monk can move its movement, then it is no longer able to stay above the water and gets dunked. If this is the case, can the monk get back up on the water and keep moving?
One perhaps unintuitive answer is that there is actually no limit on how far the monk can move without falling, which means the monk could move across liquid until the monk needs to stop for some reason, say exhaustion, then they fall in.
Not to be absurd, but in this case, I think the monk could "ice" skate on the water, and do swirls and tricks and stuff. Okay, yes, that's actually absurd.
To summarize: how far can a 9th level monk move along a vertical surfaces and across liquids without falling?
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to the end of the monk's turn, then the monk needs to be on solid ground or fall
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the monk's movement distance, even if that leaves the monk suspended on the vertical surface or the liquid between turns
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as far as the monk wants, as long as the monk keeps moving
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something else?
Best Answer
The monk must end its movement for each turn on solid ground or fall.
Unarmored Movement, PHB p. 78, emphasis mine:
The monk doesn't fall during the move when moving this way. A character's move doesn't span turns; it's something they do during their turn. Thus, at the end of the monk's turn, their move ends, and if they aren't standing on something solid, they fall.
Also note the "on your turn" condition. A monk can't run over liquids or up walls when moving as part of a reaction during another creature's turn.
To address the examples in the question:
Yes. Their move is over, so their Unarmored Movement ability isn't preventing them from falling. Also note that a 9th level human monk will have a speed of 45 feet.
90 feet. The monk can spend one ki point and use Step of the Wind to take Dash as a bonus action, then take Dash again as their action for the turn, so they may move 90 feet in total that turn. Again, note that typically a 9th level monk would be able to move (3 x 45) = 135 feet.
That's up to the DM. They might require some or all of:
As far as they can move during their turn.
How the rules handle continuous movement
The rules actually don't specify how to handle continuous movement that extends beyond a character's turn. Very long falls should take more than a turn to complete, and a character who starts a jump at the end of their turn's movement presumably doesn't lose all momentum and stop moving.
So it's up to the DM; for jumping movement, they might rule that
Likewise for monks, the DM may rule that they can 'carry over' unused 'wall running' movement from turn to turn.
Of course, because of other aspects of the 5th Edition turn system, which allows characters to act, move, and be moved in between their turns, these options can introduce many other areas where the DM would need to make rulings. If a monk ends their turn walking on water, and they are moved by an effect such as thunderwave, are they still walking on water? Does the amount they were moved deduct from the distance they can move across water on their next turn? And so on.
My reading of the intent of the monk's Unarmed Movement feature is that it limits the distance a monk can travel up a vertical surface (or over liquid) without an intervening solid, horizontal surface. The easiest way to do that is to confine these intervals to the movement on the monk's turn.