David Anthony was found guilty a second time of killing his ex-wife and stepdaughters during a retrial of his case.
Anthony was convicted in 2002 and sentenced to death. But earlier this year, the Arizona Supreme Court granted him a new trial.
The judge on his case had allowed the jury to hear evidence that Anthony molested his step daughter during his first trial.
But the state's highest court said that evidence should not have been introduced.
Anthony's second trial went on for several weeks until he was found guilty, again, on three counts of first degree murder. The aggravation phase starts Wednesday.
Follow this story at: Closing arguments in convicted killer's retrial