How is movement determined?

[Ironhawk]

You are talking about two things in one statement. Your first question was about opposed moves. The second was about unopposed moves.

In an opposed move (army 1 moves from A->B while army 2 moves from B->A) the battle will occur randomly in province A or B.

In an unopposed move ( army 1 moves from A->B while army 2 moves from B->C) you will never have a battle. Not ever. In order to "catch" an army you must work out in your head where you predict they will move and then move there before them (so you would move to prov C, not B) to head them off.