AR's

[IDref]

Phatneff did not say that the center referee can not call offside, but should not.
In almost all pregames I've been given, or have given myself, I'm told or I tell my AR's that their primary responsibility is the offside call. Their position should be second to last defender or ball. The referee's position is not usually the one with the best position to determine if an offside infraction occured. But, upon advice from a properly placed AR, it is always the center referee who blows the whistle, stops play, and awards the indirect free kick.

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In a HS game earlier this week, the other AR clearly can not keep up with the dominating attacking team and judge offside.
Referee (knowing 90% of the play is happening in that half) shifts his positioning to be able to run close to with the defensive line on the far side from the AR. He signals to me to watch over the entire "other" half, in case of a quick clear, which he would be way out of position for.

But that can only happen because 90% of play is in one half. In a more competitive game, the referee can't afford to get so out of position and risk missing the other elements of the game, fouls misconduct etc.