The teenagers killed after the car they were driving exploded in Christchurch were Glen Mcallister, Craig Mcallister and Brooklyn Taylor.
Glen and Craig, aged 16 and 13 respectively, were brothers.
They were fleeing police late on Sunday night when they ran over police spikes and crashed into a tree before the wreck burst into flames.
In a post on Facebook, the sister of Glen and Craig said it was "hard enough" losing one brother but to lose both "has destroyed me".
"I love you both endlessly. Rest in paradise my angels."
Another user told Brooklyn to "rest easy little man. Ill see you real soon homie stay hard up there your gonna be missed."
Juanita Rose, mother of Glen and Craig, told Stuff she was in "severe shock" and called her sons her "babies, my life".
A Givealittle page has been set up to help her through "this emotionally hard time".
The page said Rose is a single mother struggling to cope with unimaginable loss.
Canterbury district commander Superintendent John Price said a disaster victim identification team would formally identify the teens in the car.
Officers who tried to rescue the trio needed medical attention after the vehicle erupted into what one witness called a "ball of fire".
The officers involved were "absolutely devastated about what happened," Price said.
"These officers did not come to work to do anything other than to keep our community safe."
The vehicle was first seen speeding in Christchurch CBD about 11.13pm on Sunday, Price said.
A pursuit was begun but abandoned "very quickly due to the manner of driving by the offending vehicle".
The car crashed after hitting police spikes laid on Blenheim Rd.
It was the third fatal crash after a police pursuit in Christchurch in less than two months.
Alexia Noble-Hazelwood, 18, died on November 16. Early on December 5, Dennis Tunnicliffe, 25, and pregnant passenger Renee Percy, 35, were killed after Tunnicliffe sped away from police before crashing into a power pole.
Price said Sunday's triple-fatal crash was "the last thing police want to see".
Such incidents were "fast-moving, unpredictable and high-pressure situations that require quick judgments".
"Ultimately, police are here to protect our community. Our staff must strike a balance between the responsibility to protect life and the duty to enforce the law."
Police Association president Chris Cahill it was a "real tragedy" that would have been "unforeseen" when laying the spikes.
Early reports suggested officers involved had "done everything right".
The Independent Police Conduct Authority and Police have been reviewing the management of instances when drivers flee.
The report was meant to be made public late last year but has been delayed until February.
A police investigation into Sunday's crash is underway.
The fatal crash following a police pursuit was the third in Christchurch in less than two months.
Alexia Noble-Hazelwood, 18, was killed when the car she was in smashed into a school building on Gloucester St, late on November 16, a Friday night.
The car had earlier been involved in a police pursuit which was abandoned just minutes before the crash.
In the early hours of Wednesday, December 5, driver Dennis Tunnicliffe, 25, and passenger Renee Percy, 35, a pregnant Christchurch mother, were killed after Tunnicliffe sped away from police before crashing into a power pole on Breezes Rd.
Police followed the car after Tunnicliffe fled but abandoned the chase after less than a minute due to the "dangerous nature of the driving".
Price said last night's triple-fatal crash was "the last thing police want to see".
"We now have families who have lost their love ones and our thoughts are with them during this difficult time.
"We are currently working to notify and support their next of kin, as well as supporting our staff involved."
These incidents were always extremely testing for police, Price said.
"They are fast-moving, unpredictable and high-pressure situations that require quick judgments.
"Ultimately, police are here to protect our community. Our staff must strike a balance between the responsibility to protect life and the duty to enforce the law."
Police Association president Chris Cahill it was a "real tragedy" that would have been "unforeseen" when laying the road spikes.
"Our thoughts go out to their families, it is a real tragedy. Even more tragic is it was avoidable, just don't drive in that manner."
Early reports suggested officers involved had "done everything right".
"They have withdrawn from the fleeing driver when they realised they were not going to stop, then used road spikes to try and deflate the tyres to slow the vehicle down.
"The results here are unforeseen, but if they hadn't taken that option and they continued to drive at that speed they posed a danger to the public."
Cahill said reports the driver and passengers were teenagers was a "real concern".
"It is all too common. [Teenage drivers] is an issue for police, they don't know who is driving the vehicle and they have got to react to what is in front of them."
Since July 2017 the Independent Police Conduct Authority and New Zealand Police have been reviewing fleeing driving events to "better understand the fleeing driver environment and police management of these events".
The report was intended to be finalised and made publicly available in late 2018, but has been delayed until February 2019.
A thorough police investigation had commenced to establish the facts of what occurred in last night's crash and determine further action, including notifying the Independent Police Conduct Authority.
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