The influence of long and short chain branches on polymer properties, such as reduction of viscosity as well as increasing activation energy of flow in comparison to linear polymers, is well understood today. On the other hand, differences in thermorheological properties of hyperbranched structures, which are statistically branched structures with degrees of branching of around 50%, and linear polymers, are still under investigation. As hyperbranched polymers are getting more and more into focus of application, e.g. as drug delivery and rheological modifiers, it is important to know the structure property relations for these complex polymers. The polymer of our interest is polyglycerol, which is a biocompatible polyether polyol with hydroxyl groups in every linear repeating unit as well as the terminal end groups. We present our recent studies on a series of linear polylglycerols and a series of hyperbranched polyglycerols with a degree of branching of 50%, both in a broad molecular weight range. By comparing the thermorheological properties of the two corresponding polymer series the influence of the branched topology on dynamics could be investigated. Glass transition temperature, viscosity, fragility and activation energy of flow will be discussed in detail with respect to the different architectures and molecular weight. Furthermore, the role of hydrogen bond interactions, which are expected due to the numerous hydroxyl groups, on the polymer dynamics will be considered in the presented work.