Q. The Mishna Berura writes that one is obligated to say kaddish yasom after aleinu in shacharis, he mentions a reason because there are pesukim in alenu. However, he doesn’t similarly mention kaddish after mincha or mariv as one of the seven obligatory kaddishim. There is another source I believe for saying 10 kaddishim a day. In a minyan where there is no current avel saying kaddish, should the minyan make sure that someone says the kaddish after alenu at mincha and/or mariv? What if none in the minyan ever lost a karov?

A. Mishna Berura (55: 5) asserts that we do not recite kaddish less than seven times a day, as the verse states (Tehilim 119: 164), “Seven times a day I praise You”. The first kaddish is after yishtabach during the Shacharis service, followed by half kaddish after the amida and before ashrei. The third is kaddish titkabel after uva letzion and the fourth one is after alenu. The fifth and sixth are before and after the amida of Mincha, The seventh is recited before the amida of Maariv. The Levush does not count the kaddish after the amida or alenu during maariv, since in principle that particular tefila was only optional.
Horav Shlomo Miller Shlit’a explained that on this count there is no kaddish after alenu in mincha, since alenu was omitted then, and said only after maariv. The number seven is mentioned also in Avudraham (p. 69) and Shibolei Haleket 8 in the Geonim’s name).
Mishna Berura (132: 19) rules that one should say kaddish after alenu since pesukim are recited. This kaddish was assigned to mourners if they are present.
Shulchan Aruch Harav (quoting Zohar) mentions ten kaddeishim a day.
According to the Arizal there are twelve kaddeishim a day, six during shacharis and six more for mincha and maariv, and there are different minhagim when to recite them (Leket Hakemach 55: 4).
Some mention fourteen or fifteen kaddeishim a day (Likutei Imrei E-l p. 28, Kovetz Ohr Yisroel 23: p. 200).
Mishna Berura (55: 1) rules that as in regard to brochos, one is enjoined not to recite more kaddeishim than necessary.
Horav Shlomo Miller’s Shlit’a opinion is that how many, which and when kadeishim are recited, and by whom, most often depends on the established minhag of the shul and what nussach they follow.
He added that if no yasom is present, no kaddish should be said, unless it is recited by one that has permission from his living parents.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a.