Pregnant Kate back home; Harry plans baby bash in Las Vegas

"I'm feeling much better thank you," said a smiling pregnant Prince William's wife Kate today after spending four days of treatment in a hospital here for acute morning sickness.

She was discharged from the King Edward VII Hospital in central London following three nights under observation and will now head to Kensington Palace for a period of rest, St James's Palace said.

Kate, 30, emerged from the private hospital looking relaxed, carrying a bouquet of yellow flowers and giving a brief smile to the waiting press before being driven away with William.

"I'm feeling much better thank you," she told waiting reporters before zipping away.

Kate, who is less than 12 weeks pregnant, will now spend time at the couple's London home to recuperate.

She was admitted on Monday after developing the condition known as hyperemesis gravidarum, and was suffering from the effects of dehydration, the Daily Mail said.

"Their Royal Highnesses would like to thank the staff at the hospital for the care and treatment the Duchess has received," St James Palace spokesman said.

Messages of support have been sent from leading figures both at home and abroad, and massed ranks of the world's media have been camped out on the pavement outside the London hospital since the news was announced.

The Prime Minister was among the first to congratulate the royal couple on Twitter. "I'm delighted... They will make wonderful parents," David Cameron said.

Labour leader Ed Miliband tweeted: "A royal baby is something the whole nation will celebrate."

The Duchess's appearance came as the furore over the hoax call that duped a nurse into revealing details about her health continues.

Two Australian radio disc jockeys impersonating Queen Elizabeth II and Prince Charles placed a prank call to the hospital early yesterday, and persuaded a nurse to tell them all about the Duchess' condition.

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