A small bud appears on the dead pope's thigh. It slowly grows into a new pope and seperates from the host body quite violently in a bloody mitosis.
It then wriggles (early-stage popes are usually wormlike and referred to as Larvae) until it plops to the floor into the Pope hat (the catalyst).
(the transformation can cease if the pope hat is not on the floor at the time of mitosis, so it is tradition to place it there.)
Its skin bubbles and writhes as it grows into an upright position. it sheds it's hundreds of legs in place of two human legs, and it's jiggly, sectioned body is replaced by a human body. It assumes a normal "human" position and sits in the last pope's chair.
There you go. A full biological study on how a new pope is "elected."
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