So... is Kurokami The Animation finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: June 19, 2009
Manga finished: April 06, 2012
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
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
Kurokami The Animation follows Keita, a high schooler plagued by tragic luck and isolated from others.
His life is upended when he encounters Kuro, a mysterious girl claiming to be a Mototsumitama, a guardian of a hidden system that balances life energy called "Terra."
Kuro explains the existence of the "Doppeliner System," where Terra is divided amongst three similar-looking individuals.
Drawn into this secret world, Keita becomes bound to Kuro through a contract, forcing them to work together. He must now navigate this dangerous new reality, dealing with the implications of his newfound connection and the forces at play.