The 41-year-old was committed to stand trial in the ACT Supreme Court on four charges related to the domestic violence attack on his ex-partner.

Police said he fatally struck Ms Costigan, 28, after he forced his way into the Calwell house where she was feeding their seven-day-old daughter in February last year.

Rappel will now avoid a trial after he pleaded guilty to murder, breaching a protection order and assault occasioning actual bodily harm before Justice John Burns on Thursday.

Ms Costigan's friends and family members packed the court and one supporter whispered "Yes!" as Rappel, who wore a suit and expressed little emotion during the appearance, admitted to the three offences.

Outside the court, Michael Costigan expressed some relief and said Rappel's guilty pleas, which came more than a year after his arrest, were "a huge step forward".

Rappel has not yet entered a plea to a charge of assault causing grievous bodily harm on Ms Costigan's sister during the attack.

That charge, and some events surrounding the murder, will be the subject of a disputed facts hearing - held when the defence and prosecution cannot agree on the details of an offence.

Prosecutor Shane Drumgold said while Rappel admitted to the assault, the defence would dispute the seriousness of the injuries he inflicted.

The court was told the two-day court hearing would include evidence from three witnesses, CCTV footage and documentation.

Barrister Steven Whybrow indicated Rappel's defence team would call medical evidence.

Court documents tendered in September said Ms Costigan had fled to the home's laundry with her baby girl when Rappel arrived at the house.

Her sister, Rikki Schmidt, tried to pull her through to the garage before Rappel allegedly struck Ms Costigan with the axe and she fell to the ground.

The axe allegedly hit the hand of Ms Schmidt at the same time and severed a tendon.

Ms Schmidt's partner Bryce Bullman then knocked the axe out of Rappel's hands.

Rappel, according to the court documents, is alleged to have said:

"I killed her, I killed her, I think I killed her."

Police arrived and arrested Rappel, who is said to have told them:

"Can I say something? I murdered someone. You're going to use everything. I'm never getting out."

"Come on lads, what do you think I'm gonna do? Plead not guilty?"

Ms Costigan's two sons, aged nine and 11, were inside the Duggan Street house at the time.

Her violent killing sent shockwaves throughout the community and triggered a powerful debate over the ACT's response to domestic violence.

Mr Costigan said his niece's family and friends would now prepare themselves for the hearing and sentence proceedings, which are expected to take place later this year.

"It's a huge relief for our family and Tara's friends that he's at least pleaded guilty to what he did."

"We're really just taking it in, it's a big relief in some sense but it's just another step in the process that hasn't finished yet.

"There's been this burdensome unknown that's been there for quite some time. It's good to finally put that to rest."

He voiced some frustration over the length of time it had taken for Rappel to plead.

"In my opinion it shouldn't take a year to admit to what you've done but obviously there was a process that they have to go through."

"How can it keep continuing on when it just seems so obvious? To be perfectly frank, I think it's a case of trying to get the greatest level of leniency in a situation that doesn't really warrant any leniency."

Mr Costigan said what his niece's two young sons witnessed during the attack was "incredibly traumatising" but family members were looking out for the physical and emotional wellbeing of all three children.

"We're a big family, and it's not just our family, it's also Tara's maternal family, we're all a big family and we're looking after each other and it's just part of the process."

Mr Costigan, who last year started the Tara Costigan Foundation to raise awareness of domestic abuse, said the case had also highlighted the need for a dedicated family violence court.

"This is a major issue in Australia," he said.

"We just can't keep going with the status quo and thinking what we've been doing has been working, because clearly it hasn't."

The matter will be back in court for a directions hearing next week.