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The boy, Kiyan, weighed in at 5 lbs., 9 oz., and measured 18½ in. long – with plenty of time to catch up to his 6'8" father.
"The baby is absolutely gorgeous and I am so excited to have seen my first grandchild!" grandmother Carmen Vazquez tells PEOPLE, adding that baby and mom are "doing fine."
On Tuesday following the Nuggets' 106-91 win over the New Orleans Hornets, Anthony told reporters that Vazquez was to have labor induced that night. "The anticipation is always high this time when you're about to have a baby and about to be a father," he confessed to the Rocky Mountain News before heading to the Denver-area hospital.
The couple, who got engaged on Christmas Day 2004, have said they plan to wed following the birth. They announced to PEOPLE in September that they were expecting a baby.
Vazquez, 27, is a veejay for MTV shows including TRL, Spring Breakdown and Direct Effect. Anthony, 22, won a bronze medal as a member of the U.S. Olympic basketball team in 2004.
