Leinster will be the first to get there unless Cardiff Blues achieve the biggest upset in a quarter-final since Northampton took temporary leave of a domestic relegation fight to shock Biarritz in the Basque heartland of San Sebastian five years ago. After their demoralising trip to Scotland last weekend, the Blues hardly appear to be in the best shape to give the holders a serious run for their money.
Friday night in Glasgow was bad enough, a 31-3 trouncing by the Warriors destroying what faint hope the Blues had of forcing their way into the PRO12 play-off equation. Saturday morning proved to be even worse for one of their second half substitutes the previous night, Gavin Henson.
His drunken behaviour led to an immediate suspension by the Blues followed 48 hours later by his sacking after an emergency management meeting. Henson's fulsome apology issued in between made no difference to an outcome which leaves him looking for his fourth club in barely twelve months.
While he was sobering up, Leinster gave a timely demonstration of their all-round ability, outplaying Munster at Thomond in a manner befitting their status as Europe's No. 1. The champions' formidable international brigade will be lining up in force on Saturday at a packed Aviva Stadium just as they did at the same place for Ireland against Wales at the start of the Six Nations in February.
Sam Warburton's shoulder operation leaves the Blues no option but to plan the giant-killing without the captain of Wales. There will also be without Jamie Roberts, a tour de force for his country in their Grand Slam campaign but laid low by a knee injury against Glasgow, only his second RaboDirect PRO12 appearance of the season.
Leinster may have been overtaken by the Ospreys in the PRO12 last month at the RDS but their home record in Europe is something else - 21 wins out of 22 with London Irish (9-12 in October 2009) the only blemish. Unless something goes badly wrong, they will enjoy the luxury of putting their feet up on Sunday to find out whether they will be going to Saracens or Clermont in the semi-final.
By then they will know which other Irish team will join them in the other half of the draw. While Ulster fret over the ankle ligament damage which threatens to keep the almighty Stephen Ferris out of their back row, Munster will bust every gut at their disposal to ensure the cavalry return in the shape of Paul O'Connell, Donnacha Ryan and Conor Murray.
When it comes to winning home quarter-finals in Europe, nobody does it better than Munster. If Ulster are to reach their first semi since winning the tournament in 1999, they must succeed where everyone else has failed, a casualty list which includes some of the best from England, Wales and France.
Northampton, Ospreys, Perpignan, Stade Francais, twice, and Biarritz have all perished in Limerick at the last-eight stage. Munster may not be the force they were when conquering Europe twice in three seasons but Europe has invariably brought out the best in them and the tournament has a long track record of rewarding home advantage when it comes to the knock-out stuff.
Over the best part of 20 seasons, almost 80 per cent of quarter-finals have been won by the home team. None of that will bother an Ulster team which has been on a roll since they destroyed Leicester 41-7 at Ravenhill in January, a bonus-point win which left the Tigers with nowhere to go in Europe.
Not for nothing, therefore, does Tony McGahan call them 'the real deal.' Munster's Australian head coach, off to join the Wallabies at the end of the season, will bank on his pack meeting fire with fire, Ronan O'Gara kicking the goals as he always does and leaving the rest to the Thomond factor.
The stakes could hardly be higher what with the winner assured the reward of a semi-final on Irish soil against Edinburgh or Toulouse. Should Michael Bradley succeed in outwitting the most successful club coach in Europe, Guy Noves, then the former Ireland scrum-half will have put Edinburgh where no Scottish team has ever been before.
The exhilarating brand of rugby which swept them from a long way behind to overhaul Racing Metro 48-47 at Murrayfield last October has made Edinburgh the stunning success story of the pool stage. Since qualifying in style with a bonus-point win over London Irish in late January, they have paid dearly for their hefty contribution to the Six Nations.
Last week's home win over the Scarlets ended a run of five defeats in a row. Some 30,000 at Murrayfield on Saturday ought to ensure that Edinburgh's biggest match doubles up as a grand occasion.
Toulouse, for once, are just happy to be there. Despite four tournament victories and six finals in all, the French emperors would not have got this far had it not been for Connacht slaying Harlequins in Galway at the last round of the pool competition in the New Year.
That explains why Toulouse could lose at home to Quins and at Gloucester and still make to the last eight. Every neutral will be rooting for a home win.