  We consider versions of the FIND algorithm where the pivot element used is
the median of a subset chosen uniformly at random from the data. For the median
selection we assume that subsamples of size asymptotic to $c \cdot n^\alpha$
are chosen, where $0<\alpha\le \frac{1}{2}$, $c>0$ and $n$ is the size of the
data set to be split. We consider the complexity of FIND as a process in the
rank to be selected and measured by the number of key comparisons required.
After normalization we show weak convergence of the complexity to a centered
Gaussian process as $n\to\infty$, which depends on $\alpha$. The proof relies
on a contraction argument for probability distributions on c{\`a}dl{\`a}g
functions. We also identify the covariance function of the Gaussian limit
process and discuss path and tail properties.
