Two-man mechanics assumed:
With runners on base, the Plate Umpire (PU) has tag-ups at third base. Base umpire (BU) has 1st & 2nd
Who has catch/no catch depends on whether there are runners or not.
It sounds complex - it really isn't - it is all detailed at this link - including what the 'cone' is: Two-man Umpire Mechanics: Roles - Responsibilities
Speaking ASA & HS, this is inaccurate.
The PU always has catch unless the BU goes out for the call (rare in 2 umpire mechanics). If more than one runner, PU has lead runner, BU has the others. On a ball to the right side, it is not uncommon for the PU to take the runner @ 1st and BU take any other runners. The umpires will communicate the deviation to make sure everything is covered.
This is baseball, not the same game or mechanics.
Fair enough. I see a lot of umpires still using this mechanic and it was how I was originally taught. That is some time ago now... Must get updated for fastpitch. My bad