  We show that the Kijowski distribution for time of arrivals in the entire
real line is the limiting distribution of the time of arrival distribution in a
confining box as its length increases to infinity. The dynamics of the confined
time of arrival eigenfunctions is also numerically investigated and
demonstrated that the eigenfunctions evolve to have point supports at the
arrival point at their respective eigenvalues in the limit of arbitrarilly
large confining lengths, giving insight into the ideal physical content of the
Kijowsky distribution.
