  Fission-fragment mass and total-kinetic-energy (TKE) distributions following
fission of even-even nuclides in the region $74 \leq Z \leq 126$ and $92 \leq N
\leq 230$, comprising 896 nuclides have been calculated using the Brownian
shape-motion method. The emphasis is the region of superheavy nuclei. To show
compatibility with earlier results the calculations are extended to include
earlier studied regions. An island of asymmetric fission is obtained in the
superheavy region, $106\leq Z\leq114$ and $162\leq N\leq 176$, where the heavy
fragment is found to be close to $^{208}$Pb and the light fragment adjusts
accordingly. Most experimentally observed $\alpha$-decay chains of superheavy
nuclei with $Z > 113 $ terminate by spontaneous fission in our predicted region
of asymmetric fission. In these cases, the pronounced large asymmetry is
accompanied by a low TKE value compatible with measurements.
