 If you liked
Darker than Black: Kuro no Keiyakusha
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 ...then you might like
Batman: Gotham Knight
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Darker Than Black may be an anime but it has elements similar to superhero/detective/supernatural shows and Batman is one of them. Darker Than Black is a great addition to watch if you like Batman especially Gotham Knight because here are the similarities:
-Hei and Bruce Wayne are on a double life as Black Reaper and Batman
-Both deal with criminals
-Both have partners
-Both deal with crime scenes
Differences:
-Hei is employed by the Syndicate to eradicate Contractors whereas Bruce Wayne takes down criminals as a vigilante
-Darker Than Black have supernatural powers and Batman deals with people with artificial powers