Her loved ones gave a searing account of the lasting trauma, distress and pain Marcus Rappel inflicted when he murdered the mother-of-three with an axe before their eyes.

Their grief triggered a courtroom apology from Rappel for the deadly domestic violence attack in Calwell, which ripped a family apart and shocked the capital last February.

"I'm so sorry and I tell Tara that every day," he said.

Ms Costigan, 28, had been granted an interim domestic violence order against her ex-partner the previous day after she had grown concerned by his increasingly abusive behaviour towards her and her family.

Rappel, 41, pleaded guilty to murder, breaching a protection order, assault occasioning grievous bodily harm and assault occasioning actual bodily harm.

His face reddened and he openly sobbed in court as his ex-partner's family read out victim impact statements during a sentencing hearing in the ACT Supreme Court on Monday.

Tara's aunt, Maria Costigan, glared at Rappel as she said his "one act of rage" had taken the life of his bubbly, vivacious niece and "changed everything".

"You were the love of her life Marcus. She adored you. Would have done anything for you. You took advantage of her beautiful nature and you tortured her," she said.

"Your filthy, jealous temper has destroyed more than one life, it has created an avalanche of destruction for many, many people."

Ms Costigan also spoke of the "phenomenal destruction" experienced by her two young sons.

"Imagine your protective mother being murdered with an axe by a raging, out-of-control monster, then watching her die right in front of your eyes," she said .

"They have a life sentence."

She read out a heart-breaking story Tara's eldest son, then aged 11, had written soon after the attack.

He thanked his mother for protecting them and saving their lives that day and told her his baby sister was OK.

"I'm sorry I didn't do anything to help you that day," he wrote. "I couldn't because I would have been hurt.

"Just the hardest thing in the universe to not have you in my life."

The boy said he worried about his sister and vowed to protect her.

A collage, made from thoughts the boys had written on paper and put in a "worry box", was tendered to the court.

Margaret Costigan stated the way Rappel had taken her granddaughter's life was so shocking: "I scarce can take it in.

"I have no heart now, just an empty space in my chest that never stops aching."

Cousin Nathan Costigan said he slept with a golf club under his bed for protection and recalled sitting with Ms Costigan's sons during their police interview.

"Hearing their stories, what they saw, will be burnt into my brain for life."

Rappel himself took to the witness box in the afternoon and told the packed public gallery he was sorry beyond words.

"I understand everything you say, I hear everything you say, I feel everything you say."

Rappel gave evidence Ms Costigan said he couldn't attend their daughter's birth or pick up his furniture from her house and he had grown angry and feared he wouldn't have a role in their daughter's life.

But prosecutor Shane Drumgold suggested there wasn't any evidence in text messages between the pair Ms Costigan had been hostile and argued Rappel had grown paranoid as he believed she'd cheated on him.

He snapped when another ex-partner with whom he had a child dumped him the day he was served with the domestic violence order.

"I just lose it, I went like a zombie."

Rappel, who had taken ice and steroids in the months before, tore the order up before he went to Bunnings and bought an axe so he could "smash the sh--" out of his furniture.

Barrister Steven Whybrow: "When did you decide to murder Tara?"

Rappel: "I didn't, I didn't."

He recalled he went to the house soon after and watched Ms Costigan run away before he struck her twice.

"As soon as I realised what I was doing I dropped the axe, I screamed 'No'. I was gone, I was gone."

The hearing continues.