Ultrafast laser systems operating with high-average power in the wavelength range from 1.9 µm to 3 µm are of interest for a wide range of applications for example in spectroscopy, material processing and as drivers for secondary sources in the XUV spectral region. In this area, laser systems based on holmium-doped gain materials directly emitting at 2.1 µm have made significant progress over the past years, however so far only very few results were demonstrated in power-scalable high-power laser geometries. In particular, the thin-disk geometry is promising for directly modelocked oscillators with high average power levels that are comparable to amplifier systems at MHz repetition rate. In this paper, we demonstrate semiconductor saturable absorber mirror (SESAM) modelocked Ho:YAG thin-disk lasers (TDLs) emitting at 2.1-µm wavelength with record-holding performance levels. In our highest average power configuration, we reach 50 W of average power, with 1.13-ps pulses, 2.11 µJ of pulse energy and ∼1.9 MW of peak power. To the best of our knowledge, this represents the highest average power, as well as the highest output pulse energy so far demonstrated from a modelocked laser in the 2-µm wavelength region. This record performance level was enabled by the recent development of high-power GaSb-based SESAMs with low loss, adapted for high intracavity power and pulse energy. We also explore the limitations in terms of reaching shorter pulse durations at high power with this gain material in the disk geometry and using SESAM modelocking, and present first steps in this direction, with the demonstration of 30 W of output power, with 692-fs pulses in another laser configuration. In the near future, with the development of a next generation of SESAM samples for this wavelength region, we believe higher pulse energy approaching the 10-µJ regime, and sub-500-fs pulses should be straightforward to reach using SESAM modelocking.