Velonica, sole daughter of Galaxy Network's president, arrives on Earth on a mission for her father's universe-dominant communications company, headquartered on Metrotopia. Her objective is to expand Galaxy Network's reach by installing a giant antenna and securing a contract with Earth's designated leader. However, Earth's lack of a single governing authority complicates her task.

Extremely self-centered and rational, Velonica frequently dismisses Earth's ways with her catchphrase, "Waste, waste! Waste!" She perceives human emotions, relationships, and laughter as illogical and unnecessary. Her initial interactions are marked by impatience and frustration as she struggles to comprehend Earth's inhabitants and social structures.

Accompanied by her robot companion Morgan, Velonica believes Earth requires Galaxy Network's technological modernization. A radar malfunction leads Morgan to mistakenly identify local boy Konpei as Earth's "owner." Velonica consequently focuses her efforts on obtaining a contract from him, a process requiring a ritual kiss. Konpei's resistance forces her to extend her stay on Earth.

During this prolonged visit, Velonica encounters unfamiliar aspects of human culture like croquettes and music. Though initially dismissed as wasteful, these experiences gradually expose her to Earth's unique customs. Interactions with Konpei and his guitar-playing friend Keiko introduce her to concepts such as friendship and simple joys.

Navigating daily life on Earth, Velonica shows subtle shifts. While maintaining her core rationalist perspective, she begins participating in local activities—like singing an advertising jingle during a makeshift séance with children—indicating a degree of adaptation. The series concludes with her departure from Earth after acknowledging its distinctiveness, though her fundamental personality remains consistent.