We present Vistribute, a framework for the automatic distribution of visualizations and UI components across multiple heterogeneous devices. Our framework consists of three parts: (i) a design space considering properties and relationships of interactive visualizations, devices, and user preferences in multi-display environments; (ii) specific heuristics incorporating these dimensions for guiding the distribution for a given interface and device ensemble; and (iii) a web-based implementation instantiating these heuristics to automatically generate a distribution as well as providing interaction mechanisms for user-defined adaptations. In contrast to existing UI distribution systems, we are able to infer all required information by analyzing the visualizations and devices without relying on additional input provided by users or programmers. In a qualitative study, we let experts create their own distributions and rate both other manual distributions and our automatic ones. We found that all distributions provided comparable quality, hence validating our framework.