From MangaHelpers:
This manga is related to the anime "World Conquest Zvezda Plot." Middle-schooler Jimon Asuta is running away from home one night when he happens across a strange girl named Hoshimiya Kate. She tells him that she is the leader of a group bent on world conquest, and he humors her. It soon becomes clear that her talk was deadly serious, and he ends up recruited into the Zvesda organization. However, another organization stands in their way, of which some of Asuta's classmates are members.