"She was a dream catch." Murderer's heartless apology letter to family of ex Tara Brown.

He chased her in her car through the Gold Coast, reaching speeds up to 100km an hour. Stopped at traffic lights, he abused her and got out of his own car to bash at her windows. Eventually, he ran her off the road and her vehicle rolled down an embankment.

When strangers saw Lionel Patea trying to break through the upturned car’s window, they thought he was attempting to free his ex-girlfriend – the mother of his child – 24-year-old Tara Brown. Instead, he grabbed a fire hydrant from the side of the road – weighing almost eight kilograms – and bashed her head in.

Brown suffered six facial and head fractures, as well as irreversible brain damage. She died in hospital the next day.

Now, Patea has pleaded guilty to her murder, been sentenced to life in prison; and he has written a letter to his victim’s family.

"The question that haunts us all - how such a tragedy like this could ever have even happened?" the letter reads.

"Unfortunately I don't have the answers and can't clarify it for myself either. I hope today in court gives everyone personally involved some sort of closure."

Throughout the investigation, Patea claimed he had no memory of the murder because he was self-medicating in the days beforehand, the Courier Mail reports.

Brown's mother, Natalie Hinton, told the court she refused to read the handwritten apology.

This morning, she told The Today Show's Lisa Wilkinson she had no intention of ever reading the note.

"His apology could have happened before his actions," Hinton said. "His apology to Tara. It's worth nothing now that she's gone."

She also said the couple's three-year-old daughter misses her mum every day.

"There is not a day go by that she doesn't ask for Tara," Hinton said. "We started with 'I miss mummy. I want mummy'. Then we moved to 'I want to see mummy'. And then just the other week, she asked me if she was was going to get a new mummy. Just like her mummy."

Sarah Ferguson and Andrew a former abuser talk about Domestic Violence in Australia. Post continues below.

The pair got together in 2011, they had a daughter in 2012 and, in 2015, Brown tried to end things. She had reportedly filed a domestic violence order against Patea in the days before his death.

"Tara was a dream catch, that one-in-a-million girl. Beautiful, gentle, warm, kind-hearted and loving," Patea's letter continued. "My own angel on earth - that is how she will always be remembered by me. That is how I want her to always be remembered by everybody else too."

"(My daughter) has lost a mum and dad. Both families lose," he wrote. "A mother, daughter, father, sister and son. There is no winning here, it's a loss for everybody involved."

Patea's letter was made public by Justice Debra Mullins after the former bikie pleaded guilty. Yesterday, he was sentenced to life in prison.

"My actions were unforgivable and I do not expect forgiveness. I am not expecting any leniency from the Crown here today either," Patea wrote. "Life is jail is only part one of my sentence. Living out our days without Tara is part two."

"The hardest sentence of all? One day I am going to have to explain to my daughter what happened to mummy," he continued.

"I will endeavour to rehabilitate whilst in custody. Maybe one day I can help prevent another occurrence like this from ever happening again."