  We study the corrections to scaling for the mass of the watershed, the bridge
line, and the optimal path crack in two and three dimensions. We disclose that
these models have numerically equivalent fractal dimensions and leading
correction-to-scaling exponents. We conjecture all three models to possess the
same fractal dimension, namely, $d_f=1.2168\pm0.0005$ in 2D and
$d_f=2.487\pm0.003$ in 3D, and the same exponent of the leading correction,
$\Omega=0.9\pm0.1$ and $\Omega=1.0\pm0.1$, respectively. The close relations
between watersheds, optimal path cracks in the strong disorder limit, and
bridge lines are further supported by either heuristic or exact arguments.
