From the Super Mario Wiki
Superstar Mario (also known as Powerful Mario) is the form Baby Mario obtains when he comes in contact with a Super Star in Super Mario World 2: Yoshi's Island, Yoshi's Island: Super Mario Advance 3, Yoshi Touch & Go, and Yoshi's Island DS. Baby Mario gets a Cape, and Yoshi turns into a giant Yoshi Egg. After the time runs out, Yoshi emerges with Baby Mario. Superstar Mario gains speed, enough to walk on walls and ceilings. He can use his cape to glide down slowly. Superstar Mario is also invincible to enemies, attacks, even hazards such as spikes and lava, but not bottomless pits. Superstar Mario looks very similar to Cape Mario from Super Mario World.
Superstar Mario in the Super Mario-Kun
Superstar Mario appears as Baby Mario's power-up in the Super Mario-Kun volume 14, the adaption of Super Mario World 2: Yoshi's Island. It enables Baby Mario to climb up walls and float as it did in the games, but also gives him super strength. The strength enables him to beat up enemies and even use boulders to hurt Mario, Luigi, and Yoshi when he gets angry.
Names in other languages