No, Karl Anderson And Arn Anderson are not related in any way, which was confirmed by Arn’s own Wikipedia page.
Despite various claims to the contrary, Arn is not a member of the Anderson family. Because of his resemblance to Ole in look and wrestling style, he was given the “Anderson” name and was initially billed as Ole Anderson’s brother, then later billed as Ole’s nephew.
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He was referred to as Flair’s cousin as well. Although Flair is not a member of the Anderson family, Anderson has known him for a very long time.