The fate of all three rests with players drawn from ten of the GUINNESS PRO12 clubs, exclusively so in Ireland's case. The Millennium Stadium has witnessed some thunderous occasions since its creation just before the end of the 20th century but nothing quite like Ireland's victory over France last Sunday.
A result which allowed the RBS 6 Nations champions to avoid the All Blacks, at least until the final assuming both get there, amounted to another triumph for all four Irish provincial teams.
Leinster provided 13 of the 23-strong cast, Munster four, Ulster four and Connacht two. For their crucial win over Samoa on Tyneside, Scotland relied almost as heavily on their two big-city GUINNESS PRO12 clubs.
Marginally more than half their 23 came from the Glasgow Warriors, the GUINNESS PRO12 champions providing a round dozen which included the game's latest centurion, Sean Lamont. Nobody could dare accuse the most durable Scottish back of lacking a sense of symmetry.
He made his first Test appearance against Samoa in June 2004 and his 100th against the same country. It turned out to be some occasion, Lamont's entry as a second-half substitute coinciding with Scotland completing their recovery to clinch their quarter-final, against Australia at Twickenham on Sunday.
While Lamont acclaims the current squad as the best of all, one team-mate has a special reason for hoping that family history is about to repeat itself in this, the most surprising of Rugby World Cups.
When the Scots last won at Twickenham, way back in March 1983, they did so with a team that revolved around Roy Laidlaw at scrum-half. More than 30 years later, Sunday's team will revolve around another Laidlaw at scrum-half, Roy's nephew Greig.
His match-winning haul of a try and eight goals has put the former Edinburgh No.9 out in front as the tournament's leading point-scorer with 60, five more than Wallabies fly half Bernard Foley.
Wales go into action at Twickenham 24 hours before the Scots knowing that they ought to have beaten the Springboks during the countries' only previous World Cup collision, in Wellington four years ago when they deserved better than to lose by the narrowest possible margin.
No contender has had to cope with recurring injury on such a scale as the Welsh, still aiming for back-to-back semi-finals despite losing Leigh Halfpenny, Scott Williams, Hallam Amos, Jonathan Davies, Cory Allen and, most recently, Liam Williams.
Having hobbled out of last Saturday's near-miss against Australia, Williams' misfortune has meant a reprieve for another GUINNESS PRO12 player, Ospreys wing Eli Walker who had been in the squad only for injury to force him out before he could add to his one appearance, against Ireland in August.
All three quarter-finals involving the GUINNESS PRO12 countries will evoke memories, painful and otherwise, from past Rugby World Cups. This is how they lined-up for the most recent encounters:
Ireland against Argentina, Paris, 2007, lost 15-30:
Ireland: G Murphy; S Horgan, B O'Driscoll, G D'Arcy, D Hickie; R O'Gara, E Reddan; M Horan, J Flannery, J Hayes; D O'Callaghan, P O'Connell; S Easterby, D Wallace, D Leamy. Substitutes: R Best, B Young, M O'Kelly, N Best, I Boss, Paddy Wallace, G Duffy.
Argentina: S Corleto; L Borges, M Contepomi, F Contepomi, H Agulla; J-M Hernandez, A Pichot; R Roncero, M Ledesma, M Scelzo; I Fernandez-Lobbe, P Albacete; L Ostiglia, J-M Fernandez Lobbe, E Longo.
Wales against South Africa, Wellington 2011, lost 16-17:
Wales: J Hook; G North, J Davies, J Roberts, Shane Williams; R Priestland, M Phillips; P James, H Bennett, A Jones; L Charteris, A-W Jon es; D Lydiate, S Warburton, capt., T Faletau.
Substitutes: L Burns, R Bevington, B Davies, A Powell, T Knoyle, Scott Williams, L Halfpenny.
South Africa: F Steyn; JP Pietersen, J Fourie, J de Villiers, B Habana; M Steyn, F du Preez; B Mtawarira, J Smit, capt., J du Plessis; D Rossouw, V Matfield; H Brussow, S Burger, P Spies.
Substitutes: B du Plessis, G Steenkamp; CJ van der Linde, J Muller, W Alberts, D Hougaard, B James.
Scotland against Australia, Brisbane 2003, lost 16-33
Scotland: G Metcalfe; S Danielli, G Townsend, A Henderson, K Logan; C Paterson, B Redpath, capt; T Smith, G Bulloch, B Douglas; N Hines, S Grimes; J White, C Mather, S Taylor.
Substitutes: R Russell, G McIlwham, S Murray, J Petrie, M Blair, J McLaren, B Hinshelwood.
Australia: M Rogers; W Sailor, S Mortlock, E Flatley, L Tuqiri; S Larkham, G Gregan. Capt.; B Young, B Cannon, B Darwin; J Harrison, N Sharpe; G Smith, P Waugh, D Lyons.
Substitutes: J Paul, a Baxter, D Vickerman, M Cockbain, C Whitaker, M Giteau, J Roff.
The complete World Cup head-to-head:
Ireland v Argentina:
October 6, 2007, Paris, pool stage: Argentina 30, Ireland 15.
October 26, 2003, Adelaide, pool stage: Ireland 16, Argentina 15.
October 20, 1999, Lens, quarter-final play-off: Argentina 28, Ireland 24.
Scotland v Australia:
November 9, 2003, Brisbane, quarter-final: Australia 33, Scotland 16.
Wales v South Africa:
September 11, 2011, Wellington, pool stage: South Africa 17, Wales 16.
France v New Zealand:
June 20, 1987, Auckland, final: New Zealand 29, France 9.
October 31, 1999, Twickenham, semi-final: France 43, New Zealand 31.
November 20, 2003, Sydney: Bronze play-off: New Zealand 40, France 13.
October 6, 2007, Cardiff, quarter-final: France 20, New Zealand 18.
September 24, 2011, Auckland, pool stage: New Zealand 37, France 17.
October 23, 2011, Auckland, final: New Zealand 8, France 7.
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