"We're still working on a name. So we'll have that as soon as we can," William told scores of reporters gathered outside St. Mary's Hospital as he cradled the child.
The young family's debut public appearance was the moment the world's media had been waiting for, but the royal couple showed no sign of stress in the face of dozens of flashing cameras. Instead the couple, both 31, laughed and joked with reporters as they took turns holding their baby son, who appeared to doze through it all.
"He's got her looks, thankfully," William said, referring to his wife, the Duchess of Cambridge, as the newborn prince squirmed in his arms and poked a tiny hand out of his swaddling blanket, almost like a little royal wave.
"He's got a good pair of lungs on him, that's for sure," William added with a grin. "He's a big boy. He's quite heavy."
The infant is third in line to become monarch one day, after his grandfather, Prince Charles, and William.
But for now, the media and the public were focused on getting all the details of new parenthood they could from the couple: How they feel, what the baby looks like, and even who changed the diapers.
Kate, wearing a simple baby blue dress, said William had already had a go at changing the first one.
"He's very good at it," she said.
Asked how she felt, she said: "It's very emotional. It's such a special time. I think any parent will know what this feeling feels like."
And William poked fun at his own lack of hair when he responded with a wink to a reporter's question about the baby's locks: "He's got way more than me, thank God."
It was a much more relaxed scene than the one when Princess Diana and Prince Charles carried their newborn son, William, out to pose for photographs on the same hospital steps in 1982.
Charles, wearing a dark suit, tie and boutonniere, spoke awkwardly to reporters. By contrast, William, dressed in jeans and a blue shirt with the sleeves rolled up, joked with the assembled media and addressed some by name. At his side, Kate waved and smiled broadly, the blue sapphire engagement ring that had been Diana's on her finger.
The photographs snapped Tuesday are likely to be reprinted for decades as the baby grows into adulthood and his role as a future king, and onlookers were elated to witness the historic moment.
"William gave us a wave as they drove away, so it was perfect. Days like this really bring the country together," said Katie Allan, 26, from Bristol, England.
The couple re-entered the hospital to place the child in a car seat before re-emerging to get into a black Range Rover. With William at the wheel, they drove away. Palace officials said they will head to an apartment in Kensington Palace and spend the night there.
The birth marks a new chapter for William and Kate, who had enjoyed a quiet life away from the public eye in Anglesey, Wales, since their wedding in April 2011.
The couple had been living in a small Welsh cottage while William -- known as Flight Lieutenant Wales -- completed his term as a search-and-rescue pilot.
Now that they are a family, they are moving to a much larger apartment in Kensington Palace in central London, where William spent most of his childhood and where it will be much more difficult to keep a low profile and avoid the press.
Earlier Tuesday, William's father, Charles, and his wife, Camilla, as well as Michael and Carole Middleton -- Kate's parents -- visited the young family at the hospital.
Charles called the baby "marvelous," while a beaming Carole Middleton described the infant as "absolutely beautiful."
It was not immediately clear when Queen Elizabeth II would meet the newborn heir. The queen was hosting a reception at Buckingham Palace Tuesday evening, and was due to leave for an annual holiday in Scotland in the coming days.
Meanwhile, much of Britain and parts of the Commonwealth were celebrating the birth of a future monarch.
News that Kate gave birth to the 8 pound, 6 ounce (3.8 kilogram) boy on Monday was greeted with shrieks of joy and applause by hundreds of Britons and tourists gathered outside the hospital's private Lindo Wing and the gates of Buckingham Palace.
Revelers staged impromptu parties, and large crowds crushed against the palace gates to try to catch a glimpse -- and a photograph -- of the golden easel placed there to formally announce the birth.
Hundreds were still lining up outside the palace gates Tuesday to get near the ornate easel.
In London, gun salutes were fired, celebratory lights came on, and bells chimed at Westminster Abbey, where William and Kate wed in a lavish ceremony that drew millions of television viewers worldwide.
The baby is just a day old -- and may not be named for days or even weeks -- but he already has a building dedicated to him.
Australian Prime Minister Kevin Rudd said an enclosure at Sydney's Taronga Park Zoo would be named after the prince as part of a gift from Australia. The government will also donate $9,300 on the young prince's behalf toward a research project at the zoo to save the endangered bilby, a rabbit-like marsupial whose numbers are dwindling in the wild.
British media joined in the celebration, with many newspapers printing souvenir editions.
"It's a Boy!" was splashed across many front pages, while Britain's top-selling The Sun newspaper temporarily changed its name to "The Son" in honor of the tiny monarch-in-waiting.
"His First Royal Wave" read the headline on the Times front page that accompanied a photo of the newborn, his tiny fist poking out from the white blanket he was swaddled in.
The birth is the latest driver of a surge in popularity for Britain's monarchy, whose members have evolved, over several decades of social and technological change, from distant figures to characters in a well-loved national soap opera.
"I think this baby is hugely significant for the future of the monarchy," said Kate's biographer, Claudia Joseph.
For some, though, it was all a bit much.
The wry front page on British satirical magazine "Private Eye" -- which simply read "Woman Has Baby" -- summed up the indifference some felt about the news.
"It's a baby, nothing else," said Tom Ashton, a 42-year-old exterminator on his way to work. "It's not going to mean anything to my life."
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