In 2005, the rivalry between the two camps came to a head. Rick Nichols, who manages Sheik Hamdan’s operations in the U.S., says the Maktoums decided that it was time to stop doing business with Coolmore for the good of the industry. “Coolmore is not doing anything to help the breed by breeding their stallions to 200 mares,” he says. “Somebody’s got to stand up to Coolmore, and the Maktoums are the only ones strong enough to do it.”

Sheik Mohammed, whose day job often requires him to serve as a diplomat between the East and West, is less forthcoming: “I have great respect for them as horse people,” he says of the Coolmore group. “They have great stallions and great mares. So they will be all right.”

KEENELAND, NOW THE world’s largest horse auction house, is still the scene of the most intense battles between the Maktoums and Coolmore. Both have huge farms—the centers of their U.S. operations—within 15 miles of each other, outside downtown Lexington. Prime bluegrass country stretches for some 140 square miles around the city, with properties owned by a mix of locals and industry titans turned horse hobbyists. Coolmore’s Ashford Stud sits along Highway 60, the Wall Street of the breeding business. Massive pillars topped with eagles hold the steel entrance gate. Beyond lie multi-spired barns with intricate stonework that look more like French country churches than stables. Deep bluegrass covers the paddocks where Magnier’s horses graze over 2,000 acres—at least during the times of the year when they’re in the Northern Hemisphere.

The Maktoum farms lie just to the east. Each brother bought his own property, starting with Sheik Maktoum’s purchase of Gainsborough in 1984. Together, the three properties—Gainsborough, Sheik Mohammed’s Darley, and Sheik Hamdan’s Shadwell—sprawl across more than 7,000 acres, making the brothers the largest family owners in the area.

Gainsborough, annexed to Darley after Sheik Maktoum’s death, serves as headquarters for family members when they come to town. Down a long driveway sits a 22-bedroom mansion (under construction to add another 10 rooms), attended to at peak times by a staff of about 30. At Darley, roomy stallion boxes with spongy flooring hold the hopes of Sheik Mohammed’s breeding empire. His top new stallion, Bernardini, commands a stud fee of $100,000, and each of the mares mating with him requires a personal sign-off from the Boss.

Driving through the tranquil beauty of Kentucky horse country, one could be in any era. Then, near Keene-land, two massive and modern shapes appear on the landscape: twin Boeing 747s bearing the flag of the U.A.E.  Resting on the tarmac of Lexington’s airport, they dominate the horizon and signal that the Maktoums have come to bid.

“Very wealthy people fly here in their Gulfstream G6s, and they think they’re pretty impressive,” says Geoffrey Russell, Keeneland’s director of sales. “Then they arrive, and there are two 747s at the end of the runway. It’s very intimidating.” And they haven’t even seen the inside of Sheik Mohammed’s jet, with lavish flower arrangements, a spiral staircase, and in the nose a master bedroom with windows on either side of a sumptuous bed, for watching the plane split the clouds.

Yet at Keeneland, Sheik Mohammed acts like just another buyer. On this September day, he’s wearing cargo khakis and a long-sleeve white shirt with hand-warmer pockets and crossed American and U.A.E. flags embroidered over his breast pocket. He looks like a lawyer taking a day off, sporting a pair of rimless glasses, his hair close-cropped. He is accompanied by the junior of his two wives, Princess Haya Bint al-Hussein, the daughter of the late king of Jordan and half-sister to the country’s current ruler, Abdullah II. She wears a white blouse, open at the neck, and boot-cut jeans. Sheik Hamdan is here as well; more reserved, he remains in a suite away from the fray. Sheik Mohammed and Princess Haya walk hand in hand, gliding through the crowd of jeans-and-sneakers-clad buyers and trainers, many wearing caps pledging allegiance to specific stallions: Vindication, Giant’s Causeway, Fusaichi Pegasus.