Y stops

I think it depends on the orders.

If you tell your unit to "march" to point z, and a province changes hands to one at peace the orders stop.

If you tell your unit to "attack" point z I think it still will attack point z regardless of ownership, unless there has been a change since I tried that last.

My experiences:

In both cases described by VorlonFCW just as in Macalex's example, and as long as X and Y have only peace status, the unit of X will stop, regardless of whether march or attack was commanded >> if the X unit is already in the province, it stops immediately, if it's still outside, it continues to the border of the province.

The stopping prevents unintended wars; AI will automatically retreat after such a situation; Players must enter a new command.
(Incidentally a further reason not to change the game that units trigger war already when they entering a country)

Not shure, but I believe if it was only a march but not an attack command and X has RoW / ShM at Y, then the X unit continues to run.

I've had it happen that with attack order my units attacked after a change of ownership.

Was at peace with the new ownership.

There also can be a distance element. If your unit comes to a halt within a couple of kilometers of a province center that is occupied by another unit then a battle may begin.

Actually, I think not, in this case. The key is whether you "tell" it to stop or not, as giving a new command while the unit is within 1000 Meters of the target will forcibly result in an interaction between the two.

The same thing applies in this case. If X and Y both reach the Z province, and both X and Y are at war with Z but at peace with each other, then X or Y (assuming that Z loses) will capture the province and the other of them (Y or X) will remain at the location. IF you had set up Z's province as a waypoint with additional movement beyond that point, AND if the other player that you are at peace with wins the province, THEN your unit will trigger war with that other unit as you move past the province control point. However, I suspect this is no longer true with a fairly recent rules change. It would be interesting to see this tested.