We present an algorithm for fast global registration of partially overlapping 3D surfaces. The algorithm operates on candidate matches that cover the surfaces. A single objective is optimized to align the surfaces and disable false matches. The objective is defined densely over the surfaces and the optimization achieves tight alignment with no initialization. No correspondence updates or closest-point queries are performed in the inner loop. An extension of the algorithm can perform joint global registration of many partially overlapping surfaces. Extensive experiments demonstrate that the presented approach matches or exceeds the accuracy of state-of-the-art global registration pipelines, while being at least an order of magnitude faster. Remarkably, the presented approach is also faster than local refinement algorithms such as ICP. It provides the accuracy achieved by well-initialized local refinement algorithms, without requiring an initialization and at lower computational cost.