DUAL mechanics, anyone?

[CecilOne]

Not "former AR", but a referee in an end position rather than a middle position. The triple or double-dual is three referees, like dual is two referees; one of whom is head referee and that has nothing to do with position.
Yes, the lead or end referee is responsible for offside and the lines and fouls more visible to him/her. The middle referee is responsible for fouls, etc. more visible to him/her, free kicks, throwins opposite the end ref, etc. "More visible" often is the result of which way the player is facing, so the middle is more likely to see handling by the defense, tackles from behind and some others.
Not "cheat to the center", but move with the play and if it is on the "far" side, being closer to it. There is no relevance to basing position on the lines or corner, just seeing the play and of course, getting close enough to the lines to know when the ball is over and who gets it. That part is like dual, but with the help of a trail who is closer to the active end of the field.
Just a note, the middle referee is expected to make fewer calls than the end referees.