The Duke and Duchess of Cambridge have left Kensington Palace with their four-day-old daughter Princess Charlotte and her elder brother George for their Norfolk home Anmer Hall.
The Duke and Duchess of Cambridge named their daughter Charlotte Elizabeth Diana in honour of the Queen and also Prince William's mother.
Bookmakers have part-suspended betting on royal baby marke. in the early hours.
Punters speculating on the gender and name of the fourth in line to the throne have overwhelmingly settled for a girl, with Alice topping the list.
Ladbrokes said it had closed most markets except for the name, where Alice leads the way as the 6/4 favourite.
Charlotte's odds have been cut in half in the last week to 3/1, and James has now overtaken Arthur as the favoured name if a little prince is welcomed into the world soon.
The Takasakiyama Natural Zoological Garden in Oita is now considering renaming Charlotte after complaints from the Japanese public.
Kensington Palace warning over 'harassment' around Sandringham where Kate and William are staying with princess Charlotte and prince George.
Naming the royal baby Charlotte Elizabeth Diana will be seen as a tribute to the Duke of Cambridge's father, mother and grandfather.