So... is Kashi no Ki Mokku finished or not?
NO, it is not finished.
Why?
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Kashi no Ki Mokku tells the tale of a wooden puppet brought to life by magic and given the chance to become a real boy.
Mokku, however, starts out with numerous flaws and struggles to understand right from wrong.
He must learn valuable life lessons and overcome his many weaknesses through challenging experiences.
The anime follows Mokku as he navigates a harsh world, facing trials and tribulations that test his character and resilience.
Ultimately, the story explores his arduous journey toward self-improvement and the potential for earning true humanity.