The murders shocked the residents of Telford
A jury at Stafford Crown Court took three-and-a-half hours to convict Azhar Ali Mehmood, 26, of the murders of his girlfriend Lucy Lowe, 16, her partially-disabled sister Sarah Lowe, 17, and her mother 49-year-old Eileen Linda Lowe.
All three victims died in the fire in Telford, Shropshire, in the early hours of 5 August 2000.
Mehmood was also convicted of the attempted murder of George Lowe, 56, the teenagers' father, who escaped the fire by climbing out a bedroom window, but was unable to save his family.
Mehmood's baby daughter Tazneem was inside at the time of the fire, but was rescued.
Mr Justice Hughes imposed three life sentences on the counts of murder and a fourth life sentence for attempted murder.
The defendant slumped forward in the dock and had to be supported by officers as the verdict was returned.
Stormy relationship
The court heard that traces of petrol were discovered in the living room and kitchen of the Lowes' home which made the fire take hold quickly, trapping the teenagers and their mother upstairs.
He and Lucy Lowe had a stormy relationship and argued frequently, sometimes about her relationships with other men during a time when they had split up, the court heard.
The court was told by Adrian Redgrave QC, prosecuting: "There had also been occasions when he had been, in one way or another, humiliated in front of others by things that Lucy had said or done. He was jealous and possessive."
CCTV footage from a petrol station near the scene of the blaze showed Mehmood's black cab on the forecourt at 0328 BST.
Timings from the emergency services also revealed that a neighbour, who called the fire brigade at 0339, saw Mehmood standing outside the property.
Long nightmare
The court was told that it was absurd to imagine that someone else had entered the house and set the blaze in the five or six minutes between Mehmood's arrival at the property and the start of the blaze.
George Lowe said in a statement after the verdict: "He (Mehmood) is alive and his family can visit him.
"I on the other hand have to visit my family in the cemetery. I will never forgive him for taking them away from me."
He said the past 15 months were a nightmare, adding he would never understand why Mehmood had started the blaze.
"I now have to try to pick up the pieces and look after the most important person in my life, Tazneem, my granddaughter. She is all I have left.
"At the moment she's too young to understand what has happened to her grandmother, auntie and mother but when the time is right I will try to explain to her what happened."