There is a Star Rod on every planet in the galaxy, if not the universe.
And on each planet, there is someone or a group of someones who use its vast power for various purposes. Take for example, in one planet, immortal star-shaped beings use their Star Rod to grant the wishes of those on the planet's surface most deserving.- Supporting this is that the planets from Kirby Super Star's Milky Way Wishes all have fountains with star rods in them.
- This nicely explains why there's a Star Rod in Paper Mario.
