We predict the formation of giant vortices in quasi-two-dimensional quantum dots at high magnetic fields, i.e., in rapidly rotating electron droplets. Our numerical results of quantum dots confined by a flat, anharmonic potential show ground states where vortices are accumulated in the center of the dot, thereby leading to large cores in the electron and current densities. The phenomenon is analogous to what was recently found in rotating Bose-Einstein condensates. The giant-vortex states leave measurable signatures in the ground-state energetics. The conditions for the giant-vortex formation as well as the internal structure of the vortex cores are discussed.
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