  The FIND algorithm (also called Quickselect) is a fundamental algorithm to
select ranks or quantiles within a set of data. It was shown by Gr\"ubel and
R\"osler that the number of key comparisons required by Find as a process of
the quantiles $\alpha\in[0,1]$ in a natural probabilistic model converges after
normalization in distribution within the c\`adl\`ag space $D[0,1]$ endowed with
the Skorokhod metric. We show that the process of the residuals in the latter
convergence after normalization converges in distribution to a mixture of
Gaussian processes in $D[0,1]$ and identify the limit's conditional covariance
functions. A similar result holds for the related algorithm QuickVal. Our
method extends to other cost measures such as the number of swaps (key
exchanges) required by Find or cost measures which are based on key comparisons
but take into account that the cost of a comparison between two keys may depend
on their values, an example being the number of bit comparisons needed to
compare keys given by their bit expansions.
