With the aim of bridging the gap between high quality reconstruction and mobile robot motion planning, we propose an efficient system that leverages the concept of adaptive-resolution volumetric mapping, which naturally integrates with the hierarchical decomposition of space in an octree data structure. Instead of a Truncated Signed Distance Function (TSDF), we adopt mapping of occupancy probabilities in log-odds representation, which allows to represent both surfaces, as well as the entire free, i.e. observed space, as opposed to unobserved space. We introduce a method for choosing resolution -on the fly- in real-time by means of a multi-scale max-min pooling of the input depth image. The notion of explicit free space mapping paired with the spatial hierarchy in the data structure, as well as map resolution, allows for collision queries, as needed for robot motion planning, at unprecedented speed. We quantitatively evaluate mapping accuracy, memory, runtime performance, and planning performance showing improvements over the state of the art, particularly in cases requiring high resolution maps.