Tokyo ESP

Urushiba Rinka was a fairly normal high school girl, though she was a bit poor and her only family was her father. Then one day, she saw a penguin and some glowing fish swimming through the sky. Rinka might have thought it was a hallucination if there hadn't been another witness with her, a boy from her school with a strangely scratched-up face.

Contact with a fish caused her to pass out, and when she awoke, she had developed the power to move through inanimate objects... such as the floor of her apartment! Later, a call from her father showed her that she was not the only one the flying fish bestowed with hard-to-control superpowers! What exactly is going on here? And does Rinka's classmate know more about this situation than he's letting on?

(Source: MangaHelpers)