  In this paper we study the generating functionals of several random packing
processes: the classical Mat\'ern hard-core model; its extensions, the
$k$-Mat\'ern models and the $\infty$-Mat\'ern model, which is an example of
random sequential packing process. We first give a sufficient condition for the
$\infty$-Mat\'ern model to be well-defined (unlike the other two, the latter
may not be well-defined on unbounded spaces). Then the generating functional of
the resulting point process is given for each of the three models as the
solution of a differential equation. Series representations and bounds on the
generating functional of the packing models are also derived. Last but not
least, we obtain moment measures and Palm distributions of the considered
packing models departing from their generating functionals.
