  We compute the Hausdorff, upper box and packing dimensions for certain
inhomogeneous Moran set constructions. These constructions are beyond the
classical theory of iterated function systems, as different nonlinear
contraction transformations are applied at each step. Moreover, we also allow
the contractions to be weakly conformal and consider situations where the
contraction rates have an infimum of zero. In addition, the basic sets of the
construction are allowed to have a complicated topology such as having fractal
boundaries. Using techniques from thermodynamic formalism we calculate the
fractal dimension of the limit set of the construction. As a main application
we consider dimension results for stochastic inhomogeneous Moran set
constructions, where chaotic dynamical systems are used to control the
contraction factors at each step of the construction.
