From Longman Dictionary of Contemporary Englishdo the rounds of somethingdo the rounds of somethingBritish English, make the rounds of something American EnglishVISIT to go around from one place to another, especially looking for work or advertising something Ryan is making the rounds of talk shows to promote her new movie. → round
Examples from the Corpus
do the rounds of something• Without references, letters may do the rounds of various desks before the correct destination is found. 