Here in Israel, at the end of Shacharit most days, and Maariv all the time, someone says Barchu. In Nusach Sefard, it's before Aleinu; after in Nusach Ashkenaz. It is generally said by someone who just said Kaddish, though if no one said it, the chazzan does.
When there are multiple people who said Kaddish, how do they know which one should say Barchu? Usually there is no conflict; someone just says it. Once in a while there'll be two, or someone will need prompting. But in the average case, who is supposed to say it, that the others let him?