The Gaon Hida, 'a"h, writes that according to the Ari z"l, the Qaddish also helps the soul rise in Heaven (as opposed to only helping alleviate the punishment in Gehinnam). As such, it would appear that the Qaddish should be read for the full twelve months after a person passes away.
The Kenesseth Haggedolah states, however, that since we fear that people will say that the person was wicked (because we say that the judgement of the wicked is twelve months in Gehinnam), the Qaddish should be read for less than twelve months.
There are different customs concerning this. Ashkenazim stop reading at the end of the eleventh month and only read it again for one day on the day of the anniversary. Sephardim stop for one week. The prevalent custom is to stop at the end of the eleventh month after Minha, and to start again one week later with the 'Arbith prayer. Others stop during the last week of the twelve months. Each one should do according to his Minhagh (custom).
There are also different customs about how the Qaddish is read every subsequent year, but we will talk about it later.
(See Ben Ish Hai, Shanah Aleph, Parashath Shemoth, Oth Yod Dahl)
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