Quartararo was unsure two days before the Grand Prix, eighth Round of the championship. He had to settle for ninth (at 628/1000th) before Saturday's third practice session.
Aleix Espargaro approached the Tuscan weekend in the most positive way. After being confirmed as "captain", for the Aprilia team's next two years, the 32 year-old Spaniard didn't drag on the track, despite being surrounded by Valentino Rossi, a young retired man standing at the edge.
Espargaro was second fastest in the first session, behind the Japanese Takaaki Nakagami (Honda LCR), then he overtook Ducati's competition in the second.
For the moment, he is ahead of Jack Miller and Francesco Bagnaia of Italy.
The Vaucluse Johann Zarco, Ducati-Pramac, held the fastest time for a while before being overtaken. He finished his session with two minor falls and was ranked 4th.
Two other Ducatis still follow: those of Enea Bastanini and Luca Marini (VR46), both from Italy.
Quartararo was the Mugello winner last year. He struggled to keep his place in the Top 10, with a time that was nearly half the track record ( 1:45.187)
"I didn’t feel good on my bike. He remarked passionately before the media that it wasn't just about speed but more feeling and confidence.
Nakagami was in the lead following the first practice session. He fell to 13th in the combined ranking of both sessions, just behind Marc Marquez, the six-time Spanish world champion (12th).
Hot Tuscan Day, which saw the arrival the first supporters to reopen Mugello after three years, was also marked with the remarkable fall in moto 3 by the Japanese Ayumu Sashaki.
After losing control of his machine during the second practice session, the 21-year old crashed and was struck by Jaume Masia from Spain, the recent winner of French Grand Prix. According to organizers, the Japanese were conscious and were taken to hospital for further medical exams.