  For cell-division processes in a window, Cowan introduced four selection
rules and two division rules each of which stands for one cell-division model.
One of these is the area-weighted in-cell model. In this model, each cell is
selected for division with a probability that corresponds to the ratio between
its area and the area of the whole window. This selected cell is then divided
by throwing a (uniformly distributed) point into the cell and drawing a line
segment through the point under a random angle with the segment ending at the
cell's boundary. For the STIT model which uses both a different selection and a
different division rule, Mart\'inez and Nagel showed that for a STIT process
{Y(t, W): t > 0} the process {exp(t) Y(exp(t), W): t real} is not only
spatially stationary but also temporally. For a continuous-time area-weighted
in-cell model it is shown by using the different and generalizing approach of a
Poisson Rain that in order to get temporal stationarity it is necessary to have
an exponential spatial expansion. For the temporal transformation it is found
that there is a strong relation between that transformation and the intensity
of the Poisson Rain in time.
