write up

a short account of the news; "the report of his speech"; "the story was on the 11 o'clock news"; "the account of his speech that was given on the evening news made the governor furious"

bring to public notice by writing, with praise or condemnation; "The New York Times wrote him up last week"; "Did your boss write you up?"

put into writing; write in complete form; "write out a contract"