what major advantages corporations have given rise to their dominance as a form of business organization?
Vertical and horizontal integration begets efficiency. Corporations grow large enough to vertically integrate; essentially buying their customers' and suppliers' businesses(either literally or in the sense that they purchase/provide so much of their product that they essentially control the company), as well as their competitors' businesses, which is horizontal integration. To consolidate so many businesses, processes and resources like that helps them become enormously efficient and then offer their goods or services for the lowest cost.
This creates barriers to entry for other businesses.
Think of Wal-Mart. They have mastered their supply-chain system and buy soooo much of other companies' products that they can sell it for the lowest price. This attracts just about everybody, smaller businesses don't survive, and it prospers further.