[Lurking Libertarian]

Where do you see that all petitions for writs of certiorari are acted/voted upon by the full court?

The part where it says "the Clerk will distribute the petition, brief in opposition, and any reply brief to the Court for its consideration."

[BuckeyeTexan]

The clerk will distribute (refer, hand, submit) the petition to the Court. That doesn't mean the clerk has the authority to distribute a case for conference by the full Court. Only justices may send a case to conference and even that is done according to seniority. The justice who sends the case to conference is the justice who leads the discussion at conference.