  Lemaitre-Tolman-Bondi models as specific spherically symmetric solutions of
general relativity simplify in their reduced form some of the mathematical
ingredients of black hole or cosmological applications. The conditions imposed
in addition to spherical symmetry turn out to take a simple form at the
kinematical level of loop quantum gravity, which allows a discussion of their
implications at the quantum level. Moreover, the spherically symmetric setting
of inhomogeneity illustrates several non-trivial properties of lattice
refinements of discrete quantum gravity. Nevertheless, the situation at the
dynamical level is quite non-trivial and thus provides insights to the anomaly
problem. At an effective level, consistent versions of the dynamics are
presented which implement the conditions together with the dynamical
constraints of gravity in an anomaly-free manner. These are then used for
analytical as well as numerical investigations of the fate of classical
singularities, including non-spacelike ones, as they generically develop in
these models. None of the corrections used here resolve those singularities by
regular effective geometries. However, there are numerical indications that the
collapse ends in a tamer shell-crossing singularity prior to the formation of
central singularities for mass functions giving a regular conserved mass
density. Moreover, we find quantum gravitational obstructions to the existence
of exactly homogeneous solutions within this class of models. This indicates
that homogeneous models must be seen in a wider context of inhomogeneous
solutions and their reduction in order to provide reliable dynamical
conclusions.
