07/23/2013 04:39 EDT | Updated 09/21/2013 05:12 EDT

Royal baby makes world debut in mother Kate's arms

Prince William and Catherine, Duchess of Cambridge, gave throngs of media and well-wishers outside St. Mary's Hospital in London as well as the world what they had long been anticipating — the world's first view of the royal couple's baby son, and the third in line to the British throne.

The Duke of Cambridge, wearing a blue shirt, and Kate, resplendent in a blue polka-dot dress, emerged from the doors of the hospital's Lindo Wing on Tuesday evening local time, with the new mother carrying the tiny prince in her arms for his first public appearance since his birth Monday. Shortly after waving to the crowd, Kate handed the baby to the doting new dad.

"It's very special," William told reporters. "I'll remind him of his tardiness when he's a bit older," he said, when asked why it took so long for the royal couple to leave the hospital.

When asked who the baby looks like, William said, "He's got her looks thankfully." To which Kate gushed, "No, no, no."

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The new family of three went back inside the hospital, and a few minutes later, William emerged carrying the baby in a car seat before they all drove off, heading to Kensington Palace.

The baby's debut came after William's father, Charles, Prince of Wales, and his wife Camilla, Duchess of Cornwall, visited the London hospital.

After about a half-hour visit, Charles and Camilla left the doors of the hospital's private Lindo Wing, with Charles saying his grandson was "doing marvellously."

Following the birth of the new prince at 4:24 p.m. BST (11:24 a.m. ET) at a weight of eight pounds, six ounces, Britons and people around the world have been joining the Royal Family in celebration. But the biggest question since then had been when will the royal baby make his public debut?

Earlier Tuesday, William and Kate were enjoying their last hours alone with their son, and in the afternoon, Kate's parents, Carole and Michael Middleton, visited the couple and their new grandson.

The Middletons spoke briefly with the media after their visit to the hospital.

"He’s absolutely beautiful," Carole Middleton said.

Kensington Palace had said Tuesday that the Duke and Duchess of Cambridge were expected to leave the hospital later in the evening "but not before 6 p.m." local time (1 p.m. ET), or Wednesday morning.

"Mother, son and father are all doing well this morning," a palace spokesman noted Monday.

The palace also issued a statement from William and his wife, the former Kate Middleton:

"We would like to thank the staff at the Lindo Wing and the whole hospital for the tremendous care the three of us have received. We know it has been a very busy period for the hospital and we would like to thank everyone — staff, patients and visitors — for their understanding during this time."

The name of the royal couple's first-born, and third great-grandchild of Queen Elizabeth, remains a mystery, with the palace saying Monday there's "no news on names."

However, the baby, third in the line of succession after Prince Charles and William, will carry the title "His Royal Highness Prince [insert name] of Cambridge."

British Prime Minister David Cameron paid tribute to the royal couple by saying, "They'll make wonderful parents."

After an impromptu party at Buckingham Palace, more celebrations were held Tuesday, including a 62-gun salute outside the Tower of London to mark the arrival of the royal baby. Riders in uniform will trot past the palace to Green Park, where six field guns will fire 41 blank rounds.

The baby 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 the country. The government would donate 10,000 Australian dollars 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.

The prince's name, when known, would be added to the bilby enclosure.

"I don't know if the Royal Family would need this, but we'll probably give them a free pass to Taronga Park Zoo as well," Rudd said.

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In Canada, Prime Minister Stephen Harper hailed the arrival of "a future sovereign of Canada," and said he's looking forward to seeing the new son of the Duke and Duchess of Cambridge.

Canada's tribute to the birth of the future king included the CN Tower and Niagara Falls getting awash in blue on Monday evening.

Cian Horrobin, a spokesman for the Monarchist League, said the birth marked the beginning of a lifelong relationship for Canadians with "this boy who will one day be our king."

Massive interest in the royal birth stems from the popularity of Kate and William, who have helped make the monarchy "cool,"

British royal commentator and author Richard Fitzwilliams told CBC News on Tuesday.

The couple has "enormous public support worldwide," and the baby is "a mix between the new and the old," Fitzwilliams said, adding that the royal couple's wedding on April 29, 2011, helped rejuvenate the institution of the monarchy.

Even those opposed to the monarchy welcomed the prince's arrival.

Tom Freda, director of the organization Citizens for a Canadian Republic, said any news involving the Royal Family renews the debate over the relevance of a monarchist system, "and debate is good."

In New Zealand, royalist group Monarchy New Zealand said it had organized a national lightshow, with 40 buildings across the island lit up in blue to commemorate the royal birth, including Sky Tower in Auckland, the airport in Christchurch, and Larnach Castle in the South Island city of Dunedin.

British media joined in the celebration.

"It's a Boy!" was splashed across many U.K. front pages, while the Sun newspaper temporarily changed its name to "The Son" in honour of the tiny monarch-in-waiting.