More than 60 residential care establishments are involved in the inquiry
They are among more than 100 locations where abuse is alleged to have taken place, with boarding schools, and institutions run by religious orders and local authorities also being investigated.
The list includes Prince Charles's former school, Gordonstoun, in Morayshire, and Fettes College in Edinburgh, known as "Scotland's Eton" and which was attended by former prime minister Tony Blair.
The details emerged yesterday as chairman Lady Smith told a preliminary hearing in Edinburgh that the inquiry will be fully independent.
The list of establishments includes Prince Charles's old school
Her comments came as it emerged the inquiry's former chairman, Susan O'Brien, is suing SNP ministers for £500,000 amid claims that they forced her from the role.
The respected QC stood down last summer claiming that she was being undermined and blaming political interference.
However, successor Lady Smith said: "I see to it that the inquiry operates independently – independently of central government, independently of local government, independently of the police, independently of the prosecution services and independently of any other organisation, whether based here in Scotland or elsewhere.
"Had I had any concerns about its ability do so, I would not have accepted this appointment."
Prince Charles in pictures Fri, December 16, 2016
Prince Charles as he tours the world for his royal visits.
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Prince of Wales in Clarence House, London as he records a special message for BBC Radio 4's Just a Minute as it enters its 50th anniversary year which will be aired on Christmas Day
Aside from Gordonstoun and Fettes, other schools being investigated include Merchiston Castle School in Edinburgh, Loretto School in Musselburgh, East Lothian, and Morrison's Academy in Crieff, Perthshire.
We are determined to find out the truth about what happened to children in care
Faith-based organisations being looked at include those run by religious orders including the Benedictines, Sisters of Nazareth and the Christian Brothers. The inquiry is also investigating the relationship between the Catholic Church and these religious orders.
Three establishments run by the Church of Scotland will also be covered.
The Scottish Child Abuse Inquiry – expected to last four years – is examining historical allegations of the abuse of children in care and has been taking statements from witnesses since last spring.
Fettes College in Edinburgh is known as Scotland's Eton and was attended by Tony Blair
Lady Smith told the hearing at Parliament House that the inquiry is "determined to get to the bottom of any systemic failures that occurred" and appealed to anyone with relevant evidence to come forward and speak to the inquiry.
She said: "We are determined to find out the truth about what happened to children in care, where, how and why.
"We want to find out why the abuse was not prevented, why it was not stopped, and what needs to be done to protect children in care in the future." The inquiry has been plagued by problems since it was set up in October 2015 and has already cost more than £3.5million.
The hearing came as court documents revealed that Ms O'Brien is claiming damages for breach of contract, arguing that moves to sack her after she made allegedly inappropriate comments at a training session had made her position untenable.
She left her post in July last year, a month after panel member Professor Michael Lamb resigned citing "repeated threats" to the inquiry's independence.
A Scottish Government spokesman said that ministers had "acted appropriately at all times" and "continue to be committed to the independence of the inquiry".
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