Hardly any at all. MMA fighters rarely run in training as it's over rated and hard on the knees. They'll do plenty of other exercises but from what I read, 99% don't do any running.
How much do MMA fighters run in training?
While they do not run, they do endurance and cardio related to wrestling . . . . They expend enormous amounts of energy over different variances of time with most cardio exercises done in the gym . . . I have watched a couple of these training classes and I started sweating just watching . . . Tough stuff.
They run in a equal ratio like someone is jogging for 5 to 10 minutes. Because from jogging type running they get warm-up as they are heavily involved or doing major workouts for muscle flexibility, punch power, kick boxing & much more.