- On June 27, 1947, he defeated the South-African Eric Sturgess by 8:6 7:5 6:2 in the men’s singles final at Roland Garros in Paris. Addition to this title, with his fellow Hungarian Zsuzsa Körmöczy, he finished in the third position in mixed doubles.
- In 1948, Asbóth reached the semifinal in Wimbledon (Men’s singles) as the only European.
- In 1948, he won the Monte-Carlo tennis championship (Monte Carlo Masters).
- His win-loss at Davis Cup is 24-17 (in men’s singles 18-12, men’s doubles 6-5), best result: Semifinal (European Zone) in 1949;
- 13 times champion in Men’s singles (3rd of all-time in Hungary, eternal champion – honorary title)
- 10 times champion in Men’s doubles
- 5 times champion in Mixed doubles