Prosecutions have not been ruled out for those continuing to name the man accused of Grace Millane's murder, with the Solicitor-General tasked with contempt of court and police monitoring the ongoing breaches.
There are also fears in the legal community the continuous publication of the 26-year-old's name and details have already compromised a potential trial.
The latest example of a breach occurred when Google sent its "what's trending in New Zealand" mass email to New Zealand subscribers naming the accused.
The email also said there had been more than 100,000 searches on its search engine of the man's name.
Google is not the only internet behemoth allowing her murder accused's name to be published though, with social media platforms Twitter and Facebook also disseminating breaches.
The defendant had applied for interim name suppression when he appeared in the Auckland District Court for his first appearance on Monday.
Despite Judge Evangelos Thomas refusing to grant the application, the man's lawyer, Ian Brookie, indicated he would appeal the decision to the High Court - invoking an automatic 20-working-day suppression order.
However, since then there have been breaches by overseas media, hundreds of social media users and Google.
A spokeswoman for the Solicitor-General's office said it prosecutes contempt of court but in cases of name suppression breaches the police would prosecute.
A police spokesperson said police are "continuing to monitor the situation regarding breaches of suppression orders in New Zealand".
"At this stage, we are not aware of anyone being charged in relation to a breach of suppression order," they said.
"Police have the ability to charge a person for breaching a suppression order, provided there is sufficient evidence to do so."
Commenting on the Google mishap, Justice Minister Andrew Little told the Herald if the email was traced to any of its New Zealand infrastructure the Silicon Valley-based company could be prosecuted.
"Google has staff in New Zealand, I know because I've got Christmas cards from them," Little said.
A Google spokesperson said the company didn't know about Judge Thomas' suppression order.
But they said the tech giant would comply with any court order it was made aware of.
"We respect New Zealand law and understand the concerns around what is clearly a sensitive case," the spokesperson said.
"When we receive valid court orders, including suppression orders, we review and respond appropriately. In this case, we didn't receive an order to take action. We are looking for ways to better ensure courts have the tools to quickly and easily provide these orders to us in the future."
The spokesperson said its Google trends alerts are automatically generated by its algorithms and are based on searches over a time period in a selected geography.
Justice Minister Andrew Little said if the original breach to the British press was traced to someone who was in New Zealand at the time then they can be prosecuted.
"I'm not quite sure how much time the police want to expend trying to track who that might be," he said. "Certainly, technically, there is somebody in New Zealand who is responsible for breaching the suppression orders who could be called to account if there is a willingness to do so.
"There are plenty of people who have said, 'well this is the internet' ... but we still have to defend the basic principles of our justice system," he added, listing the presumption of innocence and the right to a fair trial.
Concerns were also raised by New Zealand Bar Association vice-president Jonathan Eaton QC, who said the breaches are not only endangering a fair trial but potentially any future trial.
"The publicity about the accused undermines the prospect of finding an impartial jury," he said.
Eaton told Newstalk ZB's Mike Hosking today that no New Zealand judge had been forced to abort a trial because of suppression breaches - but the boundaries were being pushed in the Grace Millane case.
"We will reach a stage where the court will say, 'I can no longer assure this man his fundamental right to a fair trial and the only reality is to stay the case' and we will get there.
"Just because it has been breached inappropriately is not an excuse for continual breaches and continual breaches in our view are going to put this trial at risk."
Eaton said looking up the accused's name was not a breach of suppression in itself but sharing the information was.
Earlier in the week, Prime Minister Jacinda Ardern acknowledged the online environment had evolved since Parliament last looked at suppression laws, but said there were no plans to review them.
But National MP Nick Smith labelled the suppression system "nonsense" yesterday at Parliament's justice select committee, while also mentioning the Google breach.
"The 20-day suppression order appeal mechanism is not just. Are you reconsidering [changing it] or is the Justice Ministry pretty sure there isn't a problem?" Smith asked the heads of the Justice Ministry.
"It's much better for the defendant to have their name disclosed a significant period after an awful tragedy, such as in the Millane case."
Millane was murdered on the weekend of her 22nd birthday, just a day after she arrived in Auckland as part of a one-year solo OE.
She had landed in New Zealand 10 days earlier and had been travelling around the North Island before settling in Auckland for a visit.
Her body has been returned to her family and they are in the process of taking her home to Essex in England.
Yesterday, police also found a shovel in central West Auckland which they believe is important to their case.
Detective Inspector Scott Beard said the tool was recovered by detectives as a result of the continued examination of CCTV footage.
Judge Thomas remanded the accused in custody without plea to the High Court, which told the Herald yesterday the man will now appear on January 16.