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In a message sent to his 291,000 Twitter followers about 10.15am, Taylor said: "Jonty Luteru Taylor born 16 Feb 3.06am. Mum and Jonty doing well."
Jonty was born in Hamilton's Waikato Hospital and is Taylor and wife Victoria's second child. Daughter Mackenzie was born in September 2011.
Taylor, who has been in stunning form during this year's home cricket series against West Indies and India, missed the team's test this weekend in Wellington to attend Jonty's birth.
He was tweeting updates yesterday, posting a photo of the delivery suite entrance saying, "Here we go".
Former Black Cap Scott Styris replied: "Can you make it to Wellington in time for the second innings?"