Rising Ulster Rugby player Nevin Spence died on Saturday along with his brother, Graham, and his father Noel in a slurry tank accident at the farm in Hillsborough, County Down.
The 22-year-old, who represented Ulster 42 times, mainly at centre, was tipped as a future Ireland international.
A range of rugby, other sports and political figures have expressed their shock at the deaths.
Peter Robinson, Northern Ireland first minister and Martin McGuinness, deputy first minister
"This tragedy has shocked the entire community and is a terrible reminder to us all of the dangers of farming life. Our thoughts are also with farmers everywhere at this time.
"Our thoughts and prayers are with the Spence family at this extremely sad time and pass on our deepest condolences to them.
"Nevin was a rising star of local rugby and it is only a matter of months ago, in happier times, that we had the honour of hosting him and his colleagues at a reception in Parliament Buildings to celebrate the achievement of Ulster in reaching the Heineken Cup final.
"His untimely death is a blow for the game in the province and we sympathise with his teammates and everyone at Ulster Rugby who have lost a true colleague and friend."
Eamon Gilmore, Deputy Prime Minister of Irish Republic
"This was a huge tragedy for the family.
"I want to express my condolences to Mrs Spence, to the family, the two daughters. I grew up on a farm, I understand how something like this could happen. I can picture how it could happen.
"It's rocked the island as a whole because it's just so deep, it's so many members of the one family - a tragedy that occurred in a very simple way.
"It's just a huge, huge loss for this family, for their local community, for their friends, for their neighbours and, of course, it's a loss also to sport, to Ulster sport and Ulster Rugby in particular."
Edwin Poots, health minister
"It is with immense sadness that we learnt of the tragic accident which has taken the lives of three members of the Spence family.
"The loss of Nevin, our much respected former student and a role model for so many young rugby players, his brother Graham and his father Noel, is a devastating tragedy.
"Our thoughts and prayers are with the Spence family."
Edwin Poots, health minister
"While a lot of people may focus on Nevin because he played for the Ulster rugby team we do need to focus on Noel and Graham at this time.
"Noel has left a wife and two daughters, Graham a wife and two children. Whilst a place in a rugby team can be filled a place in the home of all three men will never be filled."
Brian O'Driscoll, Ireland rugby captain
"Devastating news about Nevin Spence, his dad and brother.
"What a wonderful talent he was. Thoughts and prayers go out to his family and friends."
John Dickson, Ballynahinch Rugby Club
"I was with him (Nevin) two weeks ago doing a photoshoot at the farm, to promote the Milk It web page for the Dairy Council, and we kept his brother Graham waiting for half an hour.
"Graham was keeping Nevin going that he was a gentleman farmer, who never kept time.
"I just can't contemplate how anybody could cope with this."
Theresa Villiers, Secretary of State
"I am deeply saddened by this tragedy. It will be devastating for the family and friends of those who have lost their lives and a cause of great sadness for the whole community. This loss will be particularly strongly felt across farming and sporting circles.
"I offer my heartfelt sympathy to the Spence family. My thoughts and prayers are with them".
Shane Logan, chief executive of Ulster Rugby
"I am deeply saddened by this tragic news. Nevin was a wonderful player but also a wonderful person.
"He was well liked by everyone who knew him and his loss will be deeply felt by his teammates and everyone at Ulster Rugby."
Michelle O'Neill, agriculture minister
"I am shocked and deeply saddened to learn of this terrible tragedy which has hit this hard working farming family. My thoughts and prayers are with Noel, Graham and Nevin and their family and friends at this extremely difficult time.
"I also hope and pray that Emma Spence who was also involved in this accident makes a full recovery."
Basil McCrea, Ulster Unionist assembly member
"The entire community, whether it is the rugby fraternity, or the farming community, or just the wider local community, people have such empathy with the family.
"They just don't know what to do or what to say."
David Humphreys, Ulster director of rugby
"He brought his commitment, his passion his enthusiasm every time he played.
The characteristics that he showed when he played, those were very much transmitted when into how he conducted himself off the pitch."
Harry Sinclair, Ulster Farmers' Union president
"On behalf of all our members, I would like to extend our deepest sympathies to the family involved. This news has shocked the farming community.
"Our thoughts are with the family and friends of the three men who have so tragically lost their lives."
Billy Glynn, president of the Irish Rugby Football Union
"Nevin was an outstanding young player which was evident from his progression through the representative ranks and the game has been robbed of a very talented young man.
"The rugby community in Ireland is a very close knit one and there has been widespread shock and an outpouring of grief at this news."
Rory McIlroy, golfer
"Just heard the tragic news of Nevin Spence and his family. Makes you cherish every day you have on this Earth."
Barry McGuigan, former WBA featherwight boxing champion
"Tragic news about Nevin Spence and his family, in County Down, Northern Ireland. My deepest heart felt sympathy to his family."
Shane Williams, former Wales rugby international
"My thoughts and prayers go out to the family of Nevin Spence. A tragic loss. A class act on the field also."
"We stand shoulder to shoulder with our friends in Ulster Rugby. God bless the family and friends of Nevin Spence, his brother and dad."
Ian Humphreys, London Irish, formerly of Ulster
"Devastated to hear the news about Nevin Spence and his brother and dad.
Prayers with all his family... RIP Nev, you'll never be forgotten."
Mark Allen, snooker player
"What a loss for the family and for Ulster and Irish rugby. In shock here."
Ben Foden, England rugby international
"RIP Nevin Spence and his father and brother. Thoughts are with his family, friends and team-mates at Ulster. Such a tragic accident."
George North, Wales international
"Horrendous news about Nevin Spence and family. Thoughts are with friends and family."