The final Grand National field at Aintree, led by last year's champion Corach Rambler, will be announced on Thursday.
For safety reasons, the Aintree race had 34 runners instead of 40 this year.
Corach Rambler, trained by Lucinda Russell in Scotland, tops British aspirations in an Irish-dominated competition.
Irish trainer Gordon Elliott has nine definite runners, while Willie Mullins has eight.
After Monday's confirmation stage, 51 horses remain in the competition, including 34 top-rated horses.
If the top 35 are announced on Thursday, Kitty's Light, Chambard, and Eklat De Rire, who are on the same mark, will vote randomly for the remaining two slots.
Kitty's Light, the Scottish National winner, would try to become Christian Williams' first Welsh-trained winner since Kirkland in 1905. His daughter Betsy has leukaemia.
Last month's Cheltenham Festival winner Shakem Up'Arry, owned by Harry Redknapp, requires several withdrawals to run.
Owner Ronnie Bartlett said Galvin and Stattler will only compete if the ground is soft enough after heavy rain.
Who are Grand National favourites?
The bookies have Corach Rambler at 5-1 to become the second horse after Tiger Roll to win back-to-back Nationals since Red Rum in the 1970s.
Approximately 5-1 Corach Rambler, 7-1 I Am Maximus, 9-1 Vanillier, 10-1 Meetingofthewaters. 12-1, Mr. Incredible, Panda Boy 14-1 Kitty's Light Mahler Mission 16-1 20-1 Bar.
Irish trainers dominate large jump races at Cheltenham, winning 18 of 27.
British Horseracing Authority chief executive Julie Harrington claimed the dominance was "damaging" the sport and that more needed to be done to breed, own, train, and race outstanding horses in Britain beyond Cheltenham.