"Torajima no Mî me" is a science fiction anime series set in a future where humanity has colonized multiple planets. The story revolves around Mî me, a young girl with unique abilities, who becomes the central figure in a conflict between Earth's governing body, the United Earth Federation, and a rebel faction known as the Free Orbit Alliance. Mî me's abilities, which include telepathy and the power to manipulate energy fields, make her a target for both factions, as they believe she holds the key to controlling a powerful ancient artifact known as the "Torajima Core."

The narrative begins with Mî me living a quiet life on a remote colony planet, unaware of her significance. Her life changes when the Free Orbit Alliance attacks her colony, seeking to capture her. During the attack, she is rescued by a group of mercenaries led by Captain Ryu, a former Federation officer disillusioned with the government's oppressive policies. Ryu and his crew, including the skilled pilot Aya and the enigmatic engineer Jiro, take Mî me under their protection, embarking on a journey to uncover the truth about her powers and the Torajima Core.

As the story progresses, Mî me learns about her origins and the experiments conducted on her as a child, which granted her abilities. The Torajima Core, an ancient device capable of immense destruction or salvation, becomes the focal point of the conflict. The Federation seeks to use it to maintain control over the colonies, while the Free Orbit Alliance aims to harness its power to overthrow the Federation. Mî me's connection to the Core grows stronger as she discovers her role in its activation, leading to a climactic confrontation between the factions.

Throughout the series, the characters grapple with themes of identity, loyalty, and the consequences of wielding power. Mî me's journey is one of self-discovery, as she struggles to understand her place in the conflict and the moral implications of her abilities. The series balances action-packed sequences with moments of introspection, exploring the personal stakes for each character. By the conclusion, Mî me must make a pivotal decision that will determine the fate of humanity and the galaxy, leaving a lasting impact on the world she inhabits.