Hawke's Bay mothers who had mentioned the royal birth had said they were happy their birth wasn't so closely scrutinised, Ms Mollmann said.
"They couldn't imagine having the eyes of the world on them.
"It's such an intimate thing to be doing giving birth - and [she's] got people camped outside the hospital trying to see what they're up to."
The birth date of the future king is likely to be shared by around 167 New Zealand babies, Statistics New Zealand has revealed.
While the name of the new prince is yet to be known, Jack, Oliver and William were the most popular names for Kiwi boys in 2012 , according to the Department of Internal Affairs.
"Baby boys born today in New Zealand might expect to live 90 years on average, and girls 93 years," acting government statistician Dallas Welch said.
If heredity is anything to go by, the royal baby has a good chance of living even longer than that. Queen Elizabeth II, the new prince's great-grandmother, is 87, and the Queen Mother lived to 102.
"As third in line to the throne, the new prince may have a long wait until he becomes king," Mrs Welch said.
The new prince is likely to see plenty of change over his lifetime and be part of many historic milestones. "During her reign, the Queen has seen 14 New Zealand prime ministers take office, the dollar replace the pound in New Zealand, and the All Blacks win the Rugby World Cup twice," Mrs Welch said.
When Prince William was born in 1982, the average age of New Zealand mothers giving birth was 26. That average is now 30. Meanwhile, the average age of a first-time Kiwi mother is 28 - three years shy of the Duchess of Cambridge's 31.
Also in 1982, the New Zealand population was 3.2 million. Today it's nearing 4.5 million, and in another 30 years, when the new prince may be having his first child, Stats NZ projects the population could reach 5.6 million.
Chevrolet shares royal birthday
Sheri Heather's daughter was born in Hawke's Bay only hours from the Duchess of Cambridge's son, but there was no temptation to call her Kate, she says.
While admitting she is not a huge royalist, she says she was "pretty shocked" her daughter, named Chevrolet, was born on the same day as the third in line to the British throne. And, the birthday was also shared by Ms Heather's midwife, Erin Sandilands.
"She went into labour the day before, on the 22nd, and then laboured all night," she said. "So we were at the hospital all night and she had the baby in the early hours of the morning. We were told that the boy or baby was on its way as well and we just laughed and thought: 'Oh what a hard case if they're born around the same time'. It was a special day for me, quite cool, I thought."
By the numbers
13 hours, 51 minutes daily - average time partnered mothers spend caring for their young child
6 hours, 19 minutes - average time partnered fathers spend caring for their young child
28 - average age for first-time Kiwi mothers
31 - age of Duchess of Cambridge
$0.50 - cost of a new born's nappy in New Zealand
0.15 - cost of a new born's nappy in Britain