NetJets spent the recession quietly consolidating its position as the world’s leading provider of private-jet services. If it were an airline measured by its 710-airplane fleet, NetJets would be the fourth-largest in the world. Bigger than Southwest, bigger than China Southern, bigger than Lufthansa.

A Berkshire Hathaway company, NetJets has more than 5,500 fractional owners, hundreds more customers who buy small blocks of flying hours with the company’s Marquis jet cards, and flights to 1,900 airports in 100 countries across...