Utah state code doesn't really get specific about it.
If there's a traffic sign that indicates the lane is ending, it's the drivers' responsibility to move/merge over when it's safe to do so and the road markings are appropriate (e.g., no solid line). If there's a gore area, you cannot drive through it. However, if the road markings are such that it's permissible to move over, and it's safe to do so, then that's the appropriate time. Not that it's illegal, but waiting until the last minute is neither safe nor smart. Plus, it pisses people off.
Code that comes closest to what you're asking is this:
41-6a-903. Yield right-of-way -- Vehicle turning left -- Entering or crossing highway other than from another roadway -- Merging lanes.
The operator of a vehicle:
(3) traveling in a lane that is about to merge into a continuing lane, shall yield the right-of-way to all vehicles traveling in the continuing lane and which are so close as to be an immediate hazard.
It really comes down to common sense. Wait, we're in Utah. Disregard that last statement.