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The tournament is one of the events Prince William and Kate will attend during their visit to Dunedin and Queenstown as part of their trip to Australia and New Zealand from April 7-25.
Prince George, nearly 9 months old when the family visits, will stay in Wellington at the couple's Government House base when his parents fly south.
''We're trying to make it as easy as possible for them to have regular family time with their son,'' Prime Minister John Key said.
During the couple's fleeting visit to Dunedin on April 13, they will attend a Palm Sunday church service at St Paul's Cathedral.
St Paul's Dean the Very Rev Dr Trevor James said the Royal Couple had asked to attend a normal Palm Sunday cathedral service.
After the church service, the Regal Rugby Fun Day at Forsyth Barr Stadium, which will be free to the public, is billed as ''offering the best opportunity to see the Royal Couple''.
It will feature a Rippa rugby tournament overseen by several All Blacks. The normal stadium market will also be on.
All Blacks taking part include Highlanders Aaron Smith and Ben Smith as well as former All Black Brad Thorn.
The search is now on for eight Otago Rippa rugby teams to take part.
The Duke and Duchess of Cambridge will live the fast life when they fly to Queenstown. Activities will include a Shotover Jet thrill ride and a wine-tasting visit to Amisfield winery at Lake Hayes.
The couple will stay in Queenstown overnight before travelling to Christchurch.
Royal visit April 7-16
• Prince George will accompany Duke and Duchess Of Cambridge.
• First trip down under for duchess.
• Will visit: Wellington, Blenheim, Auckland, Dunedin, Queenstown, Christchurch, Wellington.
• In Dunedin: St Paul's Cathedral service, Rippa rugby tournament at Forsyth Barr Stadium.
• In Queenstown: Wine tasting at Amisfield, trip on Shotover Jet
• Other activities while in NZ: Meet Wellington Plunket parents, visit CTV building memorial site in Christchurch, match-race on an America's Cup yacht on Auckland Harbour, open new National Cycling Centre of Excellence and Velodrome at Cambridge.
• Wellington: Monday, April 7.
• Wellington: Wednesday, April 9.
• Blenheim: Thursday, April 10.
• Auckland: Friday, April 11.
• Waikato: Saturday, April 12.
• Dunedin, Queenstown: Sunday, April 13.
• Christchurch: Monday, April 14.
• Wellington: Wednesday, April 16.
• No public engagements Tuesday, April 8, and Tuesday, April 15.