Britain's David Florence hopes to break that dominance at the London Games when the first canoe-kayak medals are decided Tuesday.
Slovakia's Martikan and Frenchman Estanguet have shared the last four Olympic titles in the canoe slalom singles, or C-1 category, winning two each, developing a more than decade-long rivalry at the games and shutting out all their other rivals for gold.
But Florence arrived at this Olympics as the top-ranked competitor in C-1.
He also became the first man to win the singles and doubles at a World Cup meet last month and despite an early struggle at the Lee Valley White Water Center outside London in Sunday's heats at the Olympics, the Scotsman is through to the semifinals and will again be roared on as the home favourite.
Florence was 13th out of 17 after the first run, but recovered to qualify fifth out of the 12 semifinalists.
"Anywhere in the top 12 sets you up pretty well for the semis," the Beijing silver medallist said. "Of course I want to be on that podium but I've just got to concentrate on my own runs."
The eight man final is also Tuesday and Florence hopes it'll see the first Olympic champion other than No. 4-ranked Martikan or No. 2-ranked Estanguet since Lukas Pollert of the former Czechoslovakia won in Barcelona two decades ago.
Atlanta '96 and Beijing 2008 gold medal winner Martikan had an even worse start in Hertfordshire, just north of London, posting the second-slowest time in the 17-man field after a 50-second gate penalty. He roared back with the fastest time overall on his second run.
His 90.56 seconds put him ahead of Benjamin Savsek of Slovenia in second. Japan's Takuya Haneda was third and Germany's Sideris Tasiadis fourth.
"It means nothing because everything goes to zero for the semifinals," Martikan said.
That's because for Martikan — and everyone else — there's no longer any room for error as the format changes in the semis to just one run down the whitewater course for a place in the final and a shot at gold.
Likewise, the final also gives competitors just one chance on the water.
Florence was fifth fastest with 93.04 in the heats while Estanguet, the 2000 and 2004 Olympic champion, was seventh with a best time of 93.24 after penalties on both his runs.
If Florence can win gold in front of his home crowd, it'll also break Slovakia's recent Olympic stranglehold in the sport.
Martikan is the reigning singles champion, while Hochshorner brothers Peter and Pavol are three-time defending champions in the canoe slalom doubles.
Florence also is competing in the doubles for Britain alongside Richard Hounslow. The canoe doubles C-2 final is Thursday.