Monday answer
According to Ryan Jordan of Backpacking Light Magazine, in the lower 48 you need to pick a spot in the southEAST corner of Yellowstone Park. On every map I own it is essentially a corner of Yellowstone park, bordering the Teton wilderness and on the Continental Divide and nothing else. Nothing but a dotted line identifying the divide. Ryan is in the business of knowing so I'm with him on the location. In spite of that it seems odd to me that in all the U.S. lower that the maximum you would have to travel is 41.6 miles to get there and back. You could do it in two days, which you couldn't do at the King ranch.
The largest ranch in the U.S. as Dan pointed out is the King ranch in Kingsville (what else) near Brownsville. A masterful story about Captain King, Texas Rangers, border disputes, Mexican acceptance, cattle breeding, and a whole lot more. There was a two volume set out about the King Ranch bound in raw hide that was written in the 50�s and now quite expensive. Some say the King ranch was the background setting for the movie Giant. The King ranch now has 825,000 acres about 1289 sq. miles, spread across several Texas counties. It used to have over a million acres and was not the largest in Texas at that time.
The largest contiguous ranch in the U.S. with one owner is the Parker Ranch on the Big Island Hawaii. It has about 225,000 acres, and runs from the top of volcanoes to the sea. Also a good story, about a man who married a Princess. But as Ken pointed out the Deseret Ranch outside Orlando now has 300,000 acres. It is run using eighty ranchers and jumps several counties (I'm supposing they are all linked together) and is owned by the Mormon Church (Does that make it tax exempt?). Since Deseret is owned by the church that makes it a single owner too. In any event, Dan gets to wear the King Gold star on the forehead, and Ken gets the Deseret Gold star. Congrats.