Tokyo ESP: Volume 1 Omnibus (Manga)

There's a New Heroine in Town.

Rinka Urushiba's world is turned upside down when she wakes up one day - after falling right through the floor.

Encouraged by another ESPer who believes that Rinka's destiny is to become a hero of justice, she soon learns to use her powers for good.  And not a moment too soon, as those with less-than-admirable ambitions descend on Tokyo with their own set of superpowers.  As the mysterious glowing fish flitting through the city skies gift powers seemingly at random, foes become friends and alliances are made and broken.

And what about that flying penguin?