By Laura Smith-Spark and Matt Smith, CNN
LONDON (CNN) — Prince William, his wife Catherine and the royal baby start their first full day at home together Wednesday, after giving the world its first glimpse of the future king as they left the hospital.
The family’s emergence Tuesday evening from the Lindo Wing of St. Mary’s Hospital marked the end of a long wait for the throngs of journalists camped outside.
There’s just one detail left to wait for now — the little prince’s name.
He and his wife are “still working on a name,” William said on the hospital steps, “so we’ll have that as soon as we can — it’s the first time we’ve seen him really, so we’re having a proper chance to catch up.”
He said the baby has a “good pair of lungs,” and added, “He’s got her looks, thankfully.”
Catherine and William took turns holding the child, wrapped in a cream-colored blanket, as they waved to well-wishers. The prince has already changed his first diaper, the couple told reporters.
“It’s very emotional. It’s such a special time,” Catherine said.
The 8-pound, 6-ounce boy was born Monday afternoon. He’s third in line, behind Charles and William, for the British throne now held by his great-grandmother, Queen Elizabeth II.
On their way out, they walked out down the same hospital steps where Diana, Princess of Wales, and Prince Charles gave the world its first look at Prince William 31 years ago.
William installed the new royal heir in a car seat in the back of a black SUV, then got behind the wheel for the trip to their residence at Kensington Palace, in London.
It’s not clear how long the new family will spend at Kensington Palace, which was William’s boyhood home.
They may decide to relocate after a few days to the home of Catherine’s parents in the village of Bucklebury, in Berkshire.
The grand apartment they will eventually move into within the palace, Apartment 1A, is still being refurbished, so William and Catherine have been living in a small cottage in the grounds.
The late Diana, Princess of Wales, moved into Kensington Palace on her marriage to Prince Charles in 1981 and brought up William and his brother Harry there. When she died in 1997, streams of mourners laid flowers and tributes outside its gates.
Tuesday, London echoed with the sound of cannon fire and peals of bells to mark the birth.
Many bets are being placed as the wait continues for the baby’s name to be announced. British bookmakers Ladbrokes have George and James as favorites Wednesday, followed by Alexander, Arthur, Louis and Henry.
William’s name was announced a few days after birth; his brother Harry’s on leaving the hospital.
Shortly before the new baby’s departure from St. Mary’s, Prince Charles stopped by for a brief visit with his first grandchild, accompanied by his wife, Camilla, the Duchess of Cornwall. He told reporters it was “marvelous.”
And Catherine’s parents, Carole and Michael Middleton, visited earlier, with Carole Middleton telling reporters the royal baby is “absolutely beautiful.”
She said both mother and baby are doing “really well” and that she and her husband were “so thrilled” at being grandparents.
“It was so exciting. It was fantastic,” said Eliza Wells, one of the well-wishers gathered outside the hospital. “The crowd erupted, because everyone’s been waiting so long for it.”
William and Catherine “both seemed very relaxed, even with the press there and the crowd,” Wells said. “They just seemed like a normal couple.”
A normal life?
Royal commentators say the Duke and Duchess of Cambridge will try to give their son as regular an upbringing as possible.
But the intense media interest in the birth of the new prince highlights the challenge his parents face in trying to protect his privacy and maintain a degree of normalcy.
“This baby has two things stopping it from being normal,” historian Kate Williams said. “Number one, it lives in a life of incredible wealth and privilege … number two, it is an incredible celebrity, and we’ve seen this with the coverage.”
But Prince William loved that his mother tried to give him as normal a childhood as possible, including trips to the cinema and an amusement park, and sending him to a local private school as a boy — “and that’s what he wants for little baby Cambridge.”
Although the excitement over his birth is not universal, there’s no doubting the level of global interest in the prince.
On Monday, there were more than 19 million Facebook interactions related to the royal baby, Facebook said. His birth also took Twitter by storm.
As well as ruling the United Kingdom, the boy could one day be king of 15 other Commonwealth countries which have the British monarch as head of state, if none changes their constitution in the meantime.
They include Australia, Canada, New Zealand, Belize and Jamaica.
CNN’s Matthew Chance contributed to this report.