News.com.au writer Andrew Koubaridis reports on the trans-Tasman tussle to decide which country is responsible for New Zealanders who break the law in Australia.

They are the criminals that no one wants.

Not their adopted country Australia, nor it seems New Zealand where they remain citizens, even though some have only very weak family ties across the Tasman.

The sensitive subject of Kiwi crims being sent across the Tasman was one of the topics New Zealand Prime Minister Jacinda Ardern raised with Prime Minister Malcolm Turnbull as the two leaders met in Sydney for their bilateral meeting today.

Ardern and her predecessor Bill English have both previously slammed the return of crims with weak ties to New Zealand. In some cases, deportees — known as "501s" — left the country as babies or had never even been there.

"No one would argue that bringing someone back to New Zealand who has never set foot in this country lends itself to an easy process of reintegration and rehabilitation," Ardern told reporters in Wellington before she flew to Sydney.

She vowed to put a moral case to Turnbull, but acknowledged it was up to Australia to determine who was allowed to stay in the country.

The New Zealand PM said there had been some examples of people with no Kiwi ties booted out of Australia who struggled to adapt to what was essentially a foreign country to them.

"So there are a few examples where we think the policy is having an effect that perhaps hasn't been intended, or certainly a negative effect from our perspective, so we'll continue to raise that," Ardern told ABC's 7.30 last night.

"I absolutely accept the Australian government is well within their rights to exercise their deportation policy as they have ... I've raised it again, as we have on previous occasions, elements of the deportation policy that have been brought to our attention."

As of late January, there were 170 New Zealanders, including 17 women, in Australian immigration detention whose visas were automatically revoked following a December 2014 crackdown on foreign-born convicted criminals.

Foreigners who have served more than 12 months in Australian jails have been steadily rounded up. Some of the Kiwis who grew up in Australia and had weak ties across the ditch have appealed their deportations.

Today Turnbull revealed just under 40 per cent of those appeals were successful.

"We have a process — this is in accordance with Australian law. The process is a fair and just one," he said, saying it was a "moral" policy.

"We entirely understand how [it is an ] issue in New Zealand. But it is our sovereign right, as it is yours, to determine whether and in what circumstances non-citizens can remain within our borders or yours in New Zealand ... It is our fundamental right and as the Prime Minister has just acknowledged, we enforce our laws to assert our sovereignty and ensure that people (who are) not Australian citizens, who commit serious offences, are deported. It does not just apply to New Zealanders. It applies to all non-citizens."

A New Zealand parliamentary committee last week was told 1023 deportees had been sent back in the last two years and 44 per cent of them had reoffended.

Among the cases that have caused alarm in New Zealand is that of Pio Steven, a 49-year-old career criminal who was set to be deported earlier this year.

He left New Zealand as a 13-month-old and has no family or friends there. According to Fairfax, he appealed to the Administrative Appeals Tribunal of Australia while locked up in western Sydney's Villawood Detention Centre but the tribunal ruled against him and ordered him out.

Another is Alex Viane. Viane, 40, was born in American Samoa and became a New Zealand citizen as a child, but never entered the country, instead living in Australia since he was a young teenager.

He had his visa cancelled last July and a as part of his appeal bid he told the tribunal his parents were Australian citizens, his partner was Australian, as was their baby.

"I am a product of Australia. I grew up in Australia and Australia is my home. I will always consider myself as an Australian," he said, according to Stuff.co.nz.

"I have no family or supportive networks in New Zealand. I have never been to New Zealand, I have no immediate family or support. I will have no hope of contributing positively to their society."

Home Affairs Minister Peter Dutton has discretionary powers to cancel the visas of people who pose a risk to the community or are deemed not of "good character".

"Entering or remaining in Australia is a privilege, and it is expected that non-citizens are, and have been, law-abiding. Visa holders must also continue to satisfy the character requirement," a fact sheet for Section 501 of the Migration Act reads.

Even if visitors pass the character test required to enter Australia, the Department of Home Affairs and Dutton "have the power to refuse or cancel a visa on the basis that a person does not pass the character test".

In the past three years, the department has been responsible for deporting more than 3000 people who it felt didn't satisfy the requirements. In 2017, 1200 non-citizens had their visas cancelled and faced deportation.

In Queensland, 300 foreign nationals were stripped of their visas last year, second only to NSW which deported 430 people.

Caleb Maraku, 19, was a recent high-profile foreigner to be kicked out of Australia for failing the character test. He appalled the country after he was filmed smiling and laughing after escaping jail for a coward punch at Schoolies on the Gold Coast last November.

Nearly 50,000 people signed an online petition urging Dutton to get involved in Maraku's case — who then cancelled Maraku's visa under his discretionary powers.

Another person deported last year was Daniel Maxwell, a New Zealander who was an accomplice in a Brisbane teenager's death.

Maxwell, 22, was caught up in a bureaucratic bungle in August last year when he was released on an 18-month suspended jail term.

The 22-year-old New Zealander was on a night out with his co-accused Armstrong Renata in January 2016 when he repeatedly tried to start fights in Brisbane's Fortitude Valley.

Eventually, they found Cole Miller, who was coward-punched by Renata and died in hospital a day later from his head injuries.

— with Natalie Wolfe