  We continue our investigation of the Kontsevich--Penner model, which
describes intersection theory on moduli spaces both for open and closed curves.
In particular, we show how Buryak's residue formula, which connects two
generating functions of intersection numbers, appears in the general context of
matrix models and tau-functions. This allows us to prove that the
Kontsevich--Penner matrix integral indeed describes open intersection numbers.
For arbitrary $N$ we show that the string and dilaton equations completely
specify the solution of the KP hierarchy. We derive a complete family of the
Virasoro and W-constraints, and using these constraints, we construct the
cut-and-join operators. The case $N=1$, corresponding to open intersection
numbers, is particularly interesting: for this case we obtain two different
families of the Virasoro constraints, so that the difference between them
describes the dependence of the tau-function on even times.
