Parametrization based methods have recently become very popular for the generation of high quality quad meshes. In contrast to previous approaches, they allow for intuitive user control in order to accommodate all kinds of application driven constraints and design intentions. A major obstacle in practice, however, are the relatively long computations that lead to response times of several minutes already for input models of moderate complexity. In this paper we introduce a novel strategy to handle highly complex input meshes with up to several millions of triangles such that quad meshes can still be created and edited within an interactive workflow. Our method is based on representing the input model on different levels of resolution with a mechanism to propagate parametrizations from coarser to finer levels. The major challenge is to guarantee consistent parametrizations even in the presence of charts, transition functions, and singularities. Moreover, the remaining degrees of freedom on coarser levels of resolution have to be chosen carefully in order to still achieve low distortion parametrizations. We demonstrate a prototypic system where the user can interactively edit quad meshes with powerful high-level operations such as guiding constraints, singularity repositioning, and singularity connections.