The Department for Education has said decisions about the position of the head teacher are the responsibility of the school governing body.
If a child is refused a place at a school by a local education authority or school governing body, parents do have a right to a formal appeals procedure, usually established by the authority.
Following the meeting, Ystrad Mynach councillor Rhianon Passmore said the authority had been working closely with the school and governing body to enable the pupils and staff to return to classes as quickly as possible.
In most cases, parents themselves might play a role on a new school's governing body but would not be involved in teaching or the running of a school.
It also said the school's governing body had lived with uncertainty about the intentions of the council and its temporary or permanent expansion for the past three years.
Ms Salway said the Bishop of Llandaff High School's governing body and headteacher had welcomed the opportunity to place an autism centre on site and had worked closely with the local education authority on the project.
In a statement, head teacher of Colmers School Barry Doherty said the governing body was concerned local people would be "very unsettled" by the plans.
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It gives authorities a duty to pay for breakfast if the governing body of a school asks for them.
It added the report acknowledged that the school has a "realistic view" of strengths and weaknesses and "recognised that, as a result of changes to the governing body" the school was "now more effective".
Robert Masters, head teacher at The Judd School, said it would make an extra 30 places available after the governing body "carefully considered KCC's urgent request and the school's limited resources".
But a 2012 Ofsted report ranked the school as "good" and described the governing body as "very effective".
The school also acknowledged last year that college sports' governing body had inquired into old allegations that players were allowed to practice and play despite being in violation of the school's drug policy.
The new governing body must create a clear accountability between school management, governors and trustees.
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Last year almost 360, 000 children played a non-contact form of the sport at school, according to USA Rugby, the sport's national governing body.
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Mr Gove set out his plans to turn the school, which has around 900 pupils, into an academy last year and replaced the governing body with an interim executive board to monitor its performance.
The school has confirmed that "a pupil has been temporarily excluded for refusing to accept the decision of the governing body".
The report led to the Welsh government and Cardiff council removing the governing body and appointing an interim executive board (IEB) for the first time in a Welsh school.
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