3 man mechanics, as taught today, have nothing to do with the batter or the number of outs.
No runners or R3 only -- A/D
R1 only -- A/deep C
R1+R2 -- A/C
R1+R2+R3 -- A/C
R2 only -- deep B/D
R2+R3 -- deep B/D
To make it simple, anytime there is a runner at first base, the first base umpire is in A.
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