Catherine leaves hospital after acute morning sickness treatment December 6, 2012 -- Updated 1126 GMT (1926 HKT) Prince WiIliam poses with his wife Catherine, Duchess of Cambridge, as they leave the hospital, on December 6, 2012. Catherine is discharged from the hospital where she was treated for acute morning sickness She was escorted by her husband, Britain's Prince William She will now undertake a period of rest, a palace spokesman said Their child will be next in line to the British throne after William London (CNN) -- Catherine, Duchess of Cambridge, left hospital Thursday morning, three days after being admitted for acute morning sickness. She emerged from the hospital accompanied by her husband Prince William and was driven away by a waiting car. A St. James's Palace spokesman said: "The Duchess of Cambridge has been discharged from the King Edward VII Hospital and will now head to Kensington Palace for a period of rest.‬‪ Their Royal Highnesses would like to thank the staff at the hospital for the care and treatment The Duchess has received. Opinion: Pregnancy and privacy News of her pregnancy was announced Monday when Catherine was admitted to King Edward VII Hospital with hyperemesis gravidarum, a condition which involves nausea and vomiting more severe than the typical morning sickness many women suffer during early pregnancy. Catherine's discharge from the hospital comes a day after two Australian DJs hit the headlines in international media over a prank call they made to her nurse. The hospital said it deeply regretted that the hoax call had been transferred to a ward in the early hours of Tuesday morning and a short conversation was held with one of the nursing staff. The conversation included some details of the duchess's condition, according to audio posted online by the DJs' Sydney-based radio station, 2Day FM. 2Day FM apologized Wednesday for a prank it said was "done with light-hearted intentions." The duchess is not yet 12 weeks pregnant, Clarence House told CNN on Monday, so the palace is not announcing a due date for the child. CNN's Max Foster contributed to this report. The fact that anyone managed to phone through to the Duchess of Cambridge's private nurse is a major breach of privacy, whether it was a joke or not.