  The ${\bf E}\times{\bf B}$ drift motion of particles in tokamaks provides
valuable information on the turbulence-driven anomalous transport. One of the
characteristic features of the drift motion dynamics is the presence of chaotic
orbits for which the guiding center can experience large-scale drifts. If one
or more exits are placed within that chaotic orbit, the corresponding escape
basins structure is complicated and, indeed, exhibits fractal structures. We
investigate those structures through a number of numerical diagnostics,
tailored to quantify the final-state uncertainty related to the fractal escape
basins. We estimate the escape basin boundary dimension through the uncertainty
exponent method, and quantify final-state uncertainty by the basin entropy and
the basin boundary entropy. Finally, we describe the so-called Wada property,
for the case of three or more escape basins. This property is verified both
qualitatively and quantitatively, using a grid approach.
