In a manner as if wholly engrossed or engaged.(adverb)
Gnu Collaboartive International Dictionary of English: licensed under The Code Project Open License (CPOL)
Use "absorbedly" in a sentence
"From their vantage point behind the bulky transformer case he could see three men absorbedly regarding a large videoscreen."
"I was puzzled over your reasons for working so absorbedly on this thing, but now I know them and I think you're wasting your time and keeping your duaghter in needless danger."
"It had been a scheme of his boyhood; he had made collections of materials for it during his first residence in Spain; and he was actually and absorbedly engaged in the composition of the first chapters, when he was sounded by Mr. Cogswell, of the Astor Library, in behalf of Mr. Prescott."