Mick Philpott, 56, and Mairead Philpott, 31, and their friend Paul Mosley, 46, now face lengthy jail terms for triggering the blaze on May 11 last year at the couple's home in Derby, in the East Midlands region of England.
They will be sentenced for manslaughter at Nottingham Crown Court later.
Prosecutors said that the couple had hatched a plan to start the fire and then rescue the children, pinning the blame on Mick Philpott's former mistress Lisa Willis. Philpott had been fighting a custody battle with Willis.
Derbyshire Police said it was the most upsetting case the force had ever dealt with.
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"This is a shocking case for everyone involved.
Six young children lost their lives needlessly in a fire and all our efforts have been focused on getting justice for those children," said assistant chief constable Steve Cotterill.
They had suspected Philpott soon after the incident when he made a television appeal seemingly overwhelmed by grief.
His former partner, Willis, had lived with the couple and slept with Philpott on alternate nights while at the house.
His wife and girlfriend were said to have lived happily with one another for a decade but Willis left Philpott three months before the deadly fire taking her five children, four of whom were fathered by him.
He had these two women, he'd been on television, he was a bit of a sort of local celebrity almost, and he probably had a great confidence that he could get away with all sorts of things," said Professor David Cantor, an investigative psychologist at the University of Huddersfield.