In a manner that is anthropomorphous; in a way that has or displays human form or characteristics.
From anthropomorphous + -ly (adverb suffix). The -ly suffix transforms adjectives into adverbs describing how something is done or exists.
When a character in fiction acts 'anthropomorphously,' it means they're acting in a distinctly human way—which is obvious for human characters but delightfully strange when it's a talking dog or intelligent robot.
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