  In this paper we discuss modified gravity models in which growth of the
curvature is dynamically restricted. To illustrate interesting features of such
models we consider a modification of two-dimensional dilaton gravity theory
which satisfies the limiting curvature condition. We show that such a model
describes two-dimensional black holes which contain the de Sitter-like core
instead of the singularity of the original non-modified theory. In the second
part of the paper we study Vaidya type solutions of the model of the limiting
curvature theory of gravity and used them to analyse properties of black holes
which are created by the collapse of null fluid. We also apply these solutions
to study interesting features of a black hole evaporation.
