Traditionally Semantic Web applications either included a web crawler or relied on external services to gain access to the Web of Data. Recent efforts have enabled applications to query the entire Semantic Web for up-to-date results. Such approaches are based on either centralized indexing of semantically annotated metadata or link traversal and URI dereferencing as in the case of Linked Open Data. By making limiting assumptions about the information space, they violate the openness principle of the Web - a key factor for its ongoing success. In this article we propose a technique called Avalanche, designed to allow a data surfer to query the Semantic Web transparently without making any prior assumptions about the distribution of the data - thus adhering to the openness criteria. Specifically, Avalanche can perform "live" (SPARQL) queries over the Web of Data. First, it gets on-line statistical information about the data distribution, as well as bandwidth availability. Then, it plans and executes the query in a distributed manner trying to quickly provide first answers. The main contribution of this paper is the presentation of this open and distributed SPARQL querying approach. Furthermore, we propose to extend the query planning algorithm with qualitative statistical information. We empirically evaluate Avalanche using a realistic dataset, show its strengths but also point out the challenges that still exist.