The Duke and Duchess of Cambridge, also known as the Baron and Baroness of Carrickfergus, welcomed the arrival of a son on Monday afternoon.
On Tuesday evening, they emerged from St Mary's Hospital in London with their new baby to cheers from well wishers.
The Duchess held her son first before passing him to William who walked forward with his wife to answer a few questions.
"He's got a good pair of lungs on him, that's for sure. He's a big boy, he's quite heavy. We are still working on a name so we will have that as soon as we can," William said.
He added: "It's the first time we have seen him really so we are having a proper chance to catch up."
Catherine said: "It's very emotional; it's such a special time. I think any parent will know what this feeling feels like."
Her husband agreed: "It's very special."
He added: "I'll remind him of his tardiness when he's a bit older. I know how long you've all been standing here so hopefully the hospital and you guys can all go back to normal now and we can go and look after him."
The Duke also joked: "He's got her looks, thankfully."
But Kate replied: "No, no, no, I'm not sure about that."
Asked a question about nappy changing, William replied "We've done that already" before Kate revealed: "He's done the first nappy already."
Asked about the baby's hair, William added: "He's got way more than me, thank God."
The young family returned home to Kensington Palace where a crowd of well-wishers cheered as they arrived.
William smiled from behind the wheel and Kate, who was sitting on the back seat, waved with her son next to her in a baby seat.
We would love to have the royals come to Carrickfergus to show off the newborn baby.
Mayor of Carrickfergus Billy Ashe
"I would love to see a whole week of celebrations," Mayor of Carrickfergus Billy Ashe told UTV on Tuesday.
"We know that the community sector are planning a few street parties."
Earlier, Kate's parents made a visit, and speaking after Carole Middleton said that the Duke and Duchess of Cambridge's baby was "absolutely beautiful", adding: "They're both doing really well - we're so thrilled."
The Prince of Wales and Duchess of Cornwall were next to visit on Tuesday afternoon. As he exited the limousine, Charles joked with the press, asking: "Have you had a long wait?"
When leaving, he described his new grandson as "marvellous".
On Tuesday, the royal parents thanked the hospital staff who delivered their baby, describing the care they received as "tremendous".
William and Kate expressed their gratitude to the medical team at the Lindo Wing after their son was born at the unit at 4.24pm on Monday, weighing 8lb 6oz.
"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," the couple said in a statement.
"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."
William and Kate stayed overnight at St Mary's Hospital in Paddington following the birth.
Meanwhile, closer to home in the Ulster Hospital, Dundonald, a little bundle of joy was welcomed into the world - sharing her birthday with the royal baby.
Darcie-Esther McCord was born on Monday to parents Janette Somerville and dad Johnathan McCord, who already have a six-year-old boy.
"I was over the moon knowing that she'd had her royal baby and I'd had my royal baby," proud mum Janette said.
"Yesterday morning, I knew that I was going up to the labour ward at some point that day and I turned the TV on and I saw that Kate was in hospital."
"So, more or less, I was saying to myself: 'Is my child going to share the same birthday as the future king or queen? And whenever I was upstairs, they started me then.
"It was only after I had Darcie-Esther that my fiancé said to me that Kate Middleton had her baby."
Janette said the birth was that little bit more special because of the royal arrival.
"It was very emotional," she added.
(Picture: The safe hands of the Duchess of Cambridge hold her son outside the Lindo Wing of St Mary's Hospital in London.)