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The senior prosecutor for the Crown Prosecution Service (CPS) Wales said Carl Mills was responsible for "starting a devastating fire" that had "distressing and tragic consequences".
The family of Kim Buckley, Kayleigh and 6-month-old Kimberley said they felt 'justice was served' as Carl Mills was jailed for 30 years.
A statement, issued on behalf of the family by Gwent police, added:
"Carl Mills starts a life sentence for three murders but for us, the family and friends of Kim, Kayleigh and Kimberley, our life sentence started on 18 September last year when three beautiful innocent people were torn from our lives."
Jealous alcoholic Carl Mills, 28, bombarded his partner with threatening texts and, convinced she was inside with another man, warned: "I will burn your house down."
Mills stood unemotional and apparently uninterested as the jury at Newport Crown Court delivered three unanimous guilty verdicts.
He then sat and listened to a family victim impact statement read out to the court by prosecutor Gregory Bull QC.
A man has been jailed for 30 years for murdering three generations of a family in a fire.
Carl Mills, 28, will serve a minimum of 30 years after burning a family to death, including grandmother Kim Buckley, 46, her daughter Kayleigh, 17, and 6-month-old Kimberley.
The blaze ripped through the family home in Coed Eva, Cwmbran, south Wales, in the early hours of September 18, last year.