Simon Cowell has said that he was "born to be a dad" and could have more children - even though he was anxious beforehand that he might like his dogs more than his offspring.
The music mogul told US TV show Extra that he'd like a brother or sister for Eric, who was born on Valentine's Day
"I was born to be a dad," the 54-year-old said.
He added: "I wouldn't rule out [more children]. Well, I got (Yorkshire terriers) Squiddly and Diddly, and I couldn't imagine Squiddly or just Diddly... I had a brother when I was younger, so I kind of think it's cool to have two or three... two."
Simon admitted that he cried at his son's birth after dashing to New York from London, where he was filming the Britain's Got Talent auditions, to be at girlfriend Lauren Silverman's side.
"I actually said to Lauren beforehand, 'What if I like the dogs more than him?' because I've never had a baby before, and she said, 'You're gonna be absolutely fine,' and then literally within seconds of him being born, I got it," he said.
Interviewed by his ex-girlfriend Terri Seymour, the X Factor judge said it had been a last-minute dash to get to the US in time for the birth.
"The phone rings at half past five in the morning, 'I'm about to give birth' (said Lauren), so we had to find a flight, which we did, and I got there with two hours to spare."
He told Extra that his mum Julie was "really excited" and touched that the couple had decided to name the baby Eric, after Simon's father, adding: "You can't get through to her on the telephone now it's permanently engaged. I think she's told the whole village where she lives."
"Lauren told her (about the name) and she was really touched by it, because we were going to call him Simon but we both thought you know this is not a good idea so we decided on Eric.
"I look at him, Eric, and I think of my dad all the time, so it's a really good thing."
He said of life since the baby was born: "Lauren's actually been crying more than Eric, so I've had to put one of those pacifiers in her which she likes - has to be fed every three hours, otherwise she gets a little bit grumpy, and Eric's absolutely fine!"