International media cooing over Neve, Donald Trump, and a new best buddy - Claire Trevett shares her diary of Jacinda Ardern's big week in New York.

MONDAY: Today Show, Peace Summit, Reception

There's a baby in the house. Baby Neve's appearance in the General Assembly for the Nelson Mandela Peace Summit got a lot of attention - and allayed the concern Ardern was going to go Michael Jackson on us over hiding Neve's face from the cameras.

Neve's face has not been visible in any photos released or put on social media by Ardern and Clarke.

Jackson went to great lengths to protect his children's identities by covering their faces with pieces of cloth when outside.

The snaps did include one rather grumpy faced Neve which even Ardern later admitted looked startlingly like Winston Churchill. Ardern said it was exactly the same expression the baby put on for her passport photo.

Alas, the New Zealand media had missed it. After queuing for hours for media registration, negotiating the morass of security, armed Secret Service personnel, cordons and scanners to watch Ardern speak, they were foiled by a piece of paper.

The media areas are all but empty, but yet another pass is needed to get into them and the bureaucrats had run out because other journalists had not returned them.

No pass, no go.

We finally get in just as Ardern winds up. This creates some sympathy for US President Donald Trump's view of the overweening bureaucracy of the UN.

Newstalk ZB's Barry Soper gets into the mood of things by having what can only be described as a Trumpesque exchange with the bureaucrats and their pieces of paper on the way out.

TUESDAY: Amanpour, Trump statement

It was all engines go at the United Nations as the people waited for the US President to deliver his annual statement.

"Not good," was Donald Trump's verdict of everything from multilateral trade to Iran.

The same could have been said of the weather outside. It was hosing down, an apocalyptic torrent, appropriate for the speech inside.

Meanwhile, Ardern was busy making new friends.

Move over Justin Trudeau, Ardern may have found a new best buddy. She spent a lot of time with Trudeau at the Commonwealth Heads of Government Meeting in April but it was Spain's new Prime Minister Pedro Sanchez she bonded with at the UN.

The 46-year-old is one of the few who has been prime minister for a shorter period than Ardern - he took over in June. Sanchez is head of the Socialist Workers' Party in Spain and Ardern is a former president of the International Union of Socialist Youth.

Dispatches from the sidelines reported they got along very well. They even swapped numbers.

WEDNESDAY: Business Forum, The Late Show

Ardern, one of the youngest leaders, is sharing a stage at the Bloomberg Business Forum with the oldest - Malaysia's Prime Minister Mahathir Mohamad, who was 92 when staged a miraculous comeback earlier this year.

Host Fareed Zakaria asks Mahathir at the end of the session what the secret to longevity and a comeback is.

Mahathir replies it involves diet and six hours sleep a night. 

Ardern gets a look of horror on her face, and says if following such a regime will ensure she becomes leader again when she is 90 "I don't want a bar of it".

She had begun the day with a trade meeting with Canada's Justin Trudeau and Chile's Sebastian Pinera. It was all very earnest and worthy, the only real colour provided by Trudeau's startling socks, a red, white and blue geometric pattern.

There was some amusement when the New Zealand contingent turned up at the next event to discover Clarke Gayford was wearing a pair with the exact same pattern. Quelle horreur.

The risk of Ardern turning up wearing the same thing as another woman leader were very slim indeed, not least because the numbers of other women leaders is very slim.

But Ardern also took the precaution of wearing New Zealand designers: Juliette Hogan, Ingrid Starnes and Kate Sylvester were the picks for New York.

It was a Juliette Hogan dress she wore later that night, when everyone went to the Ed Sullivan Theatre for the filming of the Late Show with Stephen Colbert.

There she negotiated her way around a demand to explain the laughter at Trump by her fellow leaders, by describing it as a "spontaneous murmur".

Ardern should be perhaps be thankful she was interviewed by Colbert rather than the warm-up act, Paul Mecurio, who was fast-paced, merciless, rude and very, very funny.

For those watching at home, this is how the audience is instructed to act when the cue to applaud comes: do not clap politely, but to go "cheering ... howling, spittle flying freely from your mouths, just lose your s**t".

Ardern's staff presumably took notes for party conferences.

THURSDAY: Statement at UN

It is Ardern's big day at the UN but few of her fellow leaders are there to see it for New Zealand is way down the speaking list, and once Trump left so too did the crowd.

She was up against some competition for an audience - the Senate Judiciary Committee hearing into allegations of historic sexual assault by Trump's Supreme Court nominee Brett Kavanaugh was underway.

All other eyes were busy parsing Trump's press conference from the night before.

So her first statement to the UN was delivered to a skeleton crew in the chamber, with Neve and Clarke Gayford watching from the sidelines.

The leaders' addresses are supposed to be 15 minutes, but it is not enforced and everybody knows what happens when a politician gets a microphone. Ardern kept hers to a modest 22 minutes.

At least there were no "spontaneous murmurs" or laughs.

FRIDAY: Wrapping up

Ardern has few engagements, most of her final day in New York is reserved for wrap-up media interviews.

The true public relations value of baby Neve and Ardern's time on the Late Show has become clear.

The value was not just in the four million who watch the show, but the spin-off news stories afterwards.

But it was Neve who triumphed, the toast of New York. The story of her showing appeared everywhere - Time, the major US papers such as the Washington Post, CBS, and the British news websites.

CBS news said that moment "may end up doing more good than all the big political speeches combined".

And it also paid tribute to Gayford, "quietly breaking down some gender barriers of his own, proudly changing diapers on one of the world's biggest stages".

CLARKE'S PR GOLD

While PM Jacinda Ardern delivered speeches, did three television interviews and went to innumerable meetings on the sidelines, Clarke Gayford's output consisted of changing innumerable diapers (when in New York...), knocking over a flag in front of US President Donald Trump and issuing three tweets.

Each of those tweets about Neve's adventures at the UN turned out to be PR gold and got him bang for his buck when it came to media attention.

The first showed his ID card as "spouse of the Prime Minister" and told of Neve's determination to stay awake until 3.45am on their first night.

The second was a photo of Neve's new ID card: "New Zealand First Baby" and a tale of a startled Japanese delegation walking into a meeting room while Gayford was changing a nappy.

The third informed us Neve was still on New Zealand time: "Her mum came out at 2am and busted us watching cage fighting in our underpants."

The tweets are not some careful strategy by the PM's office, but Gayford's own creations, done without vetting or even warning to Ardern's staff. Her press secretary often did not even know Gayford had tweeted until the media asked about it.

Ardern and Gayford paid for Gayford's travel themselves deciding there were not enough official spousal duties to warrant burdening the taxpayer.

If it took Neve days to adjust sleeping patterns to the different time zone, Gayford now has the joy of returning to New Zealand tomorrow [Sunday] and going through it all again.