United became the largest airline in the FREE WORLD after acquiring Capital in 1961. Aeroflot was the world's largest airline with a fleet that numbered almost 1,000 aircraft. Then, when Aeroflot fell apart, United became the world's largest.
However, there were a few years in the early 1990s when American actually surpassed United. But that was short-lived and American fell back to second largest when the San Jose, Nashville and Raleigh hubs were dismantled.