The 42-year-old woman arrested over the death of two children whose bodies were found in suitcases was discovered "hiding in an apartment" in Korea early today.

The woman was arrested in the city of Ulsan, South Korean website Chosun.com reported.

The two children who died were a girl and a boy born in 2009 and 2012, the website reported. Their genders or date of birth have not been reported until now.

The woman was apprehended at 1am Korean time (4 am NZ time) in Ulsan, a city on Korea's southeast coast, according to the local news channel YTN.

Ulsan has a population of 1.1 million people. Chosun.com reported that the woman arrived in Korea in July 2018.

After New Zealand police issued the arrest warrant for the woman, the Seoul High Court granted an extradition arrest warrant for the woman.

Korean police plan to hand over the woman to Seoul Central District Prosecutors' Office and an extradition review will be conducted at Seoul High Court.

At this High Court hearing it will be decided if the woman will be extradited back to New Zealand.

Earlier today NZ police confirmed today that the woman has been arrested over the alleged murder of the two young children whose remains were discovered in abandoned suitcases in Manurewa.

South Korean authorities arrested the woman today on a Korean arrest warrant pursuant to two charges of murder relating to the two young victims.

• Bodies found in suitcases: Relative sought by police 'could be kids' mother'
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The arrest warrant was issued by the Korean Courts as a result of a request by NZ Police for an arrest warrant under the extradition treaty between New Zealand and the Republic of Korea (South Korea).

NZ Police have applied to have her extradited back to New Zealand to face the charges and have requested that she remains in custody while awaiting the completion of the extradition process.

"To have someone in custody overseas within such a short period of time has all been down to the assistance of the Korean authorities and the co-ordination by our NZ Police Interpol staff," police said in a statement today.

"Police would also like to acknowledge the overwhelming support from the public since the commencement of a very challenging investigation.

"As the matter is now before the courts, police are not in a position to make any further comment."

Police launched a homicide investigation after the remains of a body were found at a property in Moncrieff Avenue in Clendon Park. Photo / Dean Purcell

Police would not divulge details about when the woman was due to appear in court or when they hoped she would be expected back in New Zealand, or even if the police would be travelling to South Korea for upcoming court appearances.

There are a "number of inquiries to be completed both in New Zealand and overseas", NZ police said in a statement today.

An arrest warrant was issued by the Korean courts as a result of a request from authorities in New Zealand and South Korea.

The bodies of the children, aged between five and 10, were found by those who had unwittingly bought the suitcases from a South Auckland storage unit as part of an auction for abandoned goods.

The police investigation into the case – launched after the grisly find on August 11 at a Manurewa property – saw Interpol called in.

The Safestore facility in Papatoetoe where a Clendon Park family reportedly purchased the contents of a storage locker that contained human remains, Auckland. Photo / Jed Bradley

The children's bodies had likely been stored at the Papatoetoe Safe Store storage facility for three to four years before being discovered, Detective Inspector Tofilau Faamanuia Vaaelua said at the time.

The suitcases were bought by the Manurewa residents unwittingly as part of an online auction for an abandoned storage unit.

Police later confirmed the bodies of the children in the suitcases had likely been stored at the facility for three to four years before being discovered.

On August 22, the Korean National Police Agency confirmed a female relative of children had arrived in South Korea in 2018 and had no record of leaving the country since that year.

"We confirm that she is in South Korea and that she is a New Zealand national of Korean descent," an official at the Korean National Police Agency said.

On August 26, NZ Police confirmed the remains of the two children had been identified, but due to a suppression order, they could not be named. However, other relatives of the children still living in New Zealand have been identified.

The father of the two dead children had died of cancer while living in New Zealand in late 2017.

'Tragedy for the family'

Mijin Kim, vice-president of the Korean Society of New Zealand, said it was a very sad story.

The case had been a tragedy for the family and came as a shock to the Korean community here in New Zealand.

"We are so sorry to hear about what happened to the children.

"A member of our community who has been in touch with the woman's mother has told us that since the woman's husband died in 2017, she fell into a deep depression and has received little support.

"I think this highlights the need for greater support for those in need of mental health help, both from the Government and also from within our communities."

Kim said if the woman returned to New Zealand under extradition, the Korean Society would provide whatever support she needed during the court process.

"It is a very sad story indeed and our thoughts are with everyone involved."

'People need closure'

Auckland Councillor Daniel Newman oversees the Manurewa-Papakura Ward in which the bodies were found.

He said he was extremely relieved to hear of the arrest this morning, given the toll the deaths had taken on his community.

Newman said he was impressed with the police efforts and delighted that there appeared to progress in relation to the homicides investigation," Newman said.

"We're hoping for more information [so that] we can bring whoever is responsible to account."

Newman also praised the international police coordination that had led to the arrest of the 42-year-old woman.

"For law enforcement to be operating at a global level so that there is an opportunity for people to be held accountable is fantastic. I want to thank the New Zealand Police as well their counterparts in South Korea," Newman said.

"This is a matter that needs to be resolved. The story of what happened to those young children needs to be told and I'm hopeful that that will happen soon.

"It was an appalling situation and it was a great slight on the family and the community of Clendon [Park]. So I'm very, very hopeful that this matter will be brought to a speedy conclusion because people need closure and our community needs to move on."

NZ Police Association president Chris Cahill said he couldn't speak on details of the operational side of the arrest warrant for the 42-year-old woman - but acknowledged such investigations were intricate and rare.

"Obviously this will be a really complicated and in-depth investigation," he said today.

"But an arrest shows that the police have put in some really hard yards and worked well with our international colleagues to get it to this stage."

Cahill said such international arrests and extradition processes were an "unusual and rare event" for police.

"They're also difficult because every country has different rules so it's not like there's one international set of criteria that you have to meet," Cahill said.

"So police have to understand the requirements for extradition under New Zealand law but also under the law of the [overseas] country. But also what evidential standard is required to reach in different countries.

"So it's not an easy process and different for every country you deal with."

Extradition process

Human rights and criminal barrister Dr Tony Ellis has a long history of working on extradition cases. He says it can take years to gather enough evidence for an arrest warrant and proceed through a public hearing in the relevant country to obtain an extradition order.

While New Zealand and the Republic of Korea do have an extradition treaty, he said yesterday this did not necessarily mean the process would be successful.

"Just because you've got a treaty it doesn't mean you're going to allow your citizens to be extradited. You can see with Mr Dotcom how long it's taken.

"You need to have an arrest warrant to send to the foreign country to get the extradition on the basis of an offence. Basically, the offence needs to be something where there's imprisonment of over one year and the offence is a mirror image in both countries. There's obviously murder everywhere."

Human rights and criminal barrister, Dr Tony Ellis, has a long history working on extradition cases. Photo / RNZ

Speaking before today's developments, Ellis said it was extremely hard to gauge the likelihood of a successful arrest warrant to South Korea for the extradition of the female relative of the deceased children because it was not clear how much evidence NZ Police had beyond what was already public.

"Would there be enough [evidence]? Well, possibly, but I think when the matter was taken before whatever the extradition court is in Korea - the District Court say - there would be more evidence than that: with witnesses saying 'I saw the children and they were last seen in X, Y, Z. Mrs whatever left...'

"It could be enough evidence but depending on what the [Korean relative] can say in response it might not be."

Ellis said particularly if you don't have a "death site" for where the children were allegedly murdered to investigate, it can be difficult to gather enough evidence for an arrest warrant.

"If you haven't got that, what are you investigating? ... Nobody seems to have noticed these two children have disappeared. So we don't know where the alleged murders or manslaughter, whatever the crime may be, we don't know where that is. We don't know if police are capable of finding the site, investigating it and coming up with some forensic evidence.

"I mean, it's just an Agatha Christie story at the moment, isn't it? Murder in a suitcase."

Ellis said estimating the length of time for potential extradition was a bit like the question "how long is a piece of string?"

"It may be a year. It could be a month, depending on whether people put up any defence on these things ... The other significant factor is how much money have they got. Because depending on that, you can hire a good lawyer or not."