1. Necker Island, British Virgin Islands, Sir Richard Branson The Virgin entrepreneur bought his 74-acre private paradise for $180,000 (113,000) in 1978 and, as a condition of sale, agreed to build a luxury resort. It now sleeps 28 people in 10 rooms, and rents for $62,000 (39,000) a day. For that, guests can enjoy two private beaches, pools, tennis courts, a personal chef and team of 60 staff.

2. Blackadore Caye, Belize, Leonardo DiCaprio Bought by the Wolf of Wall Street and Titanic star in 2005 for $1.75 million (1.1 million), DiCaprio, a keen environmentalist, is planning to build an eco-friendly resort on the 104 acre island near the famous barrier reef off the coast of Belize. He has said the resort will be open to the public as an example of sustainable tourism, complete with eco-tours of the island.

3. Little Halls Pond, Bahamas, Johnny Depp The actor is said to have paid $3.6 million for the 45-acre island in 2004 and renamed it after his daughter, Lily Rose. The island has six beaches and uses solar power for its energy supply. In 2009, Depp told Vanity Fair: I dont think Id ever seen any place so pure and beautiful. You can feel your pulse rate drop about 20 beats. Its instant freedom.

4. Musha Cay and the Islands of Copperfield Bay, Bahamas, David Copperfield One private island not enough for you? How about a whole chain. Magician David Copperfield owns a string of 11 islands including the largest, Musha Cay, 85 miles from Nassau in the Bahamas. A favourite with celebrities including Oprah Winfrey and Bill Gates, up to 24 guests can be accommodated at a time. Penelope Cruz and Javier Bardem were married there in 2010.

Celine Dion's island chteau

5. Ile Gagnon, Quebec, Celine Dion Situated on the Iles River, in her home state of Quebec in Canada, the singer had a stone mansion custom built for her on the 19-acre island in 2001. Ile Gagnon was put on the market for $29.6 Canadian dollars (18.6) two years ago but has yet to find a buyer.

6. St Phillips Island, South Carolina, Ted Turner Bought by the media mogul for $2 million (1.3 million) in 1979, the year before he launched CNN, the 5,000-acre St Phillips Island has two miles of beaches, maritime forests and lagoons. He also owns a 298-acre landing area on the neighbouring St Helena island.

7. Mago Island, Fiji, Mel Gibson At 8.5 square miles, Mago is one of the largest private islands in the South Pacific. It was bought by the actor for $15 million (9.4 million) in 2005 from a Japanese company. Descendants of the native inhabitants, who were relocated in the 19th century, have protested about his ownership.

8. Rooster Cay, Bahamas, Eddie Murphy The comedian paid $15 million (9.4 million) for the 15 acre island situated five minutes off the coast Nassau in 2007. He had previously owned another cay in the Bahamas, Pearl Island.

Hulopoe & Manele Bay, Lanai (Alamy)

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Top 10 millionaires' paradise islands: where the rich and famous go to get away from it all