Bishop Dermot O'Mahony, assistant from 1975 to his retirement in 1996, was aware of 13 priests in the sample of 46.
He agreed that it was "a wrong policy" to give little or no information to a parish priest about offenders assigned to their parish.
The commission also named the late James Kavanagh, a former professor of social science at UCD, who was the number two in Dublin from 1972 to 1998.
He failed to deal properly with Fr Bill Carney after he pleaded guilty to child sexual abuse, and tried to influence garda handling of criminal complaints against Fr Carney, the report said. He also persuaded a family to drop a complaint to gardai against another priest.
When "factual evidence" of Fr Thomas Naughten's "abusing emerged in another parish Bishop Murray's failure to reinvestigate the earlier suspicions was inexcusable", the report said.
Bishop Brendan Comiskey, who resigned as Bishop of Ferns in 2002 for failing to deal with pervert priests including the late Fr Sean Fortune, was aware for years of complaints or suspicions of abuse in Dublin.
Accusing religious orders of also knowing about abuse, the report says the Columban Order had "clear knowledge of complaints against one of their members, Fr Patrick Maguire".
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