If one misses Barchu at the beginning of Maariv, should one say it at the end of Maariv (as is commonly done)? If so when should it be done and who should do it?
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I have heard, in the name, if I recall correctly (but it's possible I don't), of Rabbi Avraham Pam (of Torah Vodaas), that there is no benefit in saying bar'chu after maariv after missing at the start, but that it's not a shem l'vatala, as one can technically say bar'chu at any time in the presence of a minyan.
According to Halacah Berurah 133:1
Minhag Yisrael is to say barechu after the last kaddish in Shacharit. According to the Maran Beit Yosef, and the REMA, the reason is to fulfill the obligation of people who didn't hear it already (becuase they came late). For that reason they rule not to say this barechu on Shabbat and Yom Tov, because even people who came late still arrived on time to hear barechu during keriat shema.
According to the Ari Z"L, there are kabbalistic reasons to always say barechu after the end of the tefillah, and the reasons have nothing to do with fulfilling people's obligation. (The same reasoning applies to Arvit, but not to Mincha.) This is the minhag of the Sepharadim. Kehillot who follow this minhag have barechu printed in the siddur in the proper place.
P.S. I only discuss Shacharit here, because the volume of Halacha Berurah that includes the halachot of Arvit hasn't been written yet.
What have I seen in practice? In practice at Ashkenazi synagogues in Chutz l'Aretz, someone who was late and missed barechu says barechu after Aleinu. I don't remember what the minhag is for ashkenazim in Eretz Yisrael.
In Sephardi synagogues, the mourners who said kaddish right before Aleinu say barechu right after they finish saying kaddish. If there are no mourners (and kaddish wasn't said, then the shaliach tzibbur says it right before Aleinu.) A sepharadi siddur will tell you exactly where to say it.
One of the reasons we have seven aliyos on Shabbos is for those that missed Borechu in Tefilas Shacharis to hear Borechu seven times. (will add in source later)