So... is Chobits finished or not?
It is a bit ambiguous in this case.
Why?
The anime finished before the manga:
Anime finished: September 25, 2002
Manga finished: October 28, 2002
MangaUpdates contains information about the anime adaptation and indicates that it is complete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Chobits explores the relationship between humans and advanced, human-like computers called Persocoms. Hideki, a struggling student, discovers a discarded Persocom that can only say "Chii."
As Hideki takes Chii in and teaches her about the world, he and his friends become intrigued by her unique qualities, especially the possibility she might be a legendary "Chobit" - a Persocom rumored to possess genuine emotions.
The anime follows Hideki's attempts to understand Chii, navigate his college entrance exams, and grapple with the question of whether a real connection can form between a human and a machine.
Ultimately, Chobits asks if love and affection can transcend the boundaries of technology and humanity in a world where computers are becoming indistinguishable from people.