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Alina Shah, 10, and her brother Aman, eight, died in the fire last July. Their mother, Iram, 30, died in hospital. Asjid Mahmood, 22, was found guilty of murder and his brother Arshed, 18, was found guilty of manslaughter.
Bradford Crown court heard the attack happened after a business dispute between Asjid Mahnmood and Mrs Shah's former partner and father of the two children, Zaheer Shah. Prosecutors said it centred around a car Mr Shah and Asjid Mahmood had bought together to hire out.
Asjid Mahmood admitted setting fire to petrol-soaked paper at the back door of the family's home in Hendford Drive in the early hours of 6 July last year. At the trial he claimed he was only trying to scare Mrs Shah's former husband, who had left the house earlier in the evening.
Mrs Shah suffered 80% burns in the fire and died in hospital six days later.