We present a numerical study of rapid, so called type III migration for Jupitersized planets embedded in a protoplanetary disc. We limit ourselves to the case of inward migration, and study in detail its evolution and physics, concentrating on the structure of the corotation and circumplanetary regions, and processes for stopping migration. We also consider the dependence of the migration behaviour on several key parameters. We perform this study using the results of global, two-dimensional hydrodynamical simulations with adaptive mesh refinement. The initial conditions are chosen to satisfy the condition for rapid inward migration. We find that type III migration can be divided into two regimes, fast and slow. The structure of the coorbital region, mass accumulation rate, and migration behaviour differ between these two regimes. All our simulations show a transition from the fast to the slow regime, ending type III migration well before reaching the star. The stopping radius is found to be larger for more massive planets and less massive discs. A sharp density drop is also found to be an efficient stopping mechanism. In the fast migration limit the migration rate and induced eccentricity are lower for less massive discs, but almost do not depend on planet mass. Eccentricity is damped on the migration time scale.
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