  A special type of binomial splitting process is studied. Such a process can
be used to model a high-dimensional corner parking problem, as well as the
depth of random PATRICIA tries (a special class of digital tree data
structures). The later also has natural interpretations in terms of distinct
values in iid geometric random variables and the occupancy problem in urn
models. The corresponding distribution is marked by logarithmic mean and
bounded variance, which is oscillating, if the binomial parameter $p$ is not
equal to 1/2, and asymptotic to 1 in the unbiased case. Also, the limiting
distribution does not exist owing to periodic fluctuations.
