In a manner showing complete focus and attention; with deep concentration on something.
From absorbed (past participle of absorb, from Latin absorbere: ab- 'away' + sorbere 'to suck in') plus -ly. The adverb form emphasizes the manner of being completely engaged.
When someone is staring 'absorbedly' at their phone, their brain is actually prioritizing that task so completely that they literally don't hear people calling their names—the brain filters everything else out!
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