  This work considers the behavior of the height distributions of the
equipotential lines in a region confined by two interfaces: a cathode with an
irregular interface and a distant flat anode. Both boundaries, which are
maintained at distinct and constant potential values, are assumed to be
conductors. The morphology of the cathode interface results from the deposit of
$2 \times 10^{4}$ monolayers that are produced using a single competitive
growth model based on the rules of the Restricted Solid on Solid and Ballistic
Deposition models, both of which belong to the Kadar-Parisi-Zhang (KPZ)
universality class. At each time step, these rules are selected with
probability $p$ and $q = 1 - p$. For several irregular profiles that depend on
$p$, a family of equipotential lines is evaluated. The lines are characterized
by the skewness and kurtosis of the height distribution. The results indicate
that the skewness of the equipotential line increases when they approach the
flat anode, and this increase has a non-trivial convergence to a delta
distribution that characterizes the equipotential line in a uniform electric
field. The morphology of the equipotential lines is discussed; the discussion
emphasizes their features for different ranges of $p$ that correspond to
positive, null and negative values of the coefficient of the non-linear term in
the KPZ equation.
