Not to be confused with Flying
If a Pawn transmutates into a King, this is known as Ascension. This is the most regal and thus most popular transmutation. Replace the Pawn figurine with a spare King figurine of the same colour. Your army now has two (or more?) Kings, both (all?) of whom have all the properties of a King, including Check and Checkmate.
If all of an army's Pawns become Kings without any dying, this is known as Kingapalooza. All the rest of your army's Pieces are now capable of transmutation.
If the entirety of an army become Kings without any dying, this is called Communism. If some died, this is called Applied Communism.