Engrossed means completely taken up by what you are doing. Engrossed in a book, utterly engrossed, engrossed in conversation.
It always takes in. The word has a second life in law, where to engross a document is to prepare the final formal copy, and that is the older sense — from a French phrase meaning in large writing. The everyday sense came from being wholly occupied.
1adjectiveengrossedCompletely taken up by what you are doing.
“He was so engrossed in his book that he missed his stop.”
engrossed is a state of attention.