The 87-year-old monarch made a short trip from Buckingham Palace to visit the two-day-old Prince of Cambridge, who is third in line to the throne.
The baby's name hasn't been revealed yet. "We're still working on a name," William told reporters Tuesday as he and Kate took the baby home from St. Mary's Hospital.
Bookmaker William Hill has George -- the name of six previous British kings -- as the favorite at 2-to-1 odds, with James at 4-to-1.
Images of the prince, his little hand peeking above a white crocheted wrap, blanketed the front pages of British newspapers Wednesday. The Daily Mail offered a photo album image with the headline "Baby's first royal wave."
The prince slept through his debut public appearance -- though William assured the media he had "a good pair of lungs on him."
The new family is expected to spend time quietly at Kensington Palace, their London home. As well as choosing a name, William and Kate will soon choose a photographer for the baby's first official portrait.
William has two weeks' paternity leave from his job as a Royal Air Force search-and-rescue helicopter pilot.
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