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The silicon-vertex tracker (SVT) for the BaBar Experiment at the PEP-H Asymmetric B Factory at Stanford Linear Accelerator Center (SLAC), is a five-layer double-sided ac-coupled silicon-microstrip detector. It is a crucial element for the precise measurement of the decay position of B mesons, satisfying the severe constraints imposed by the accelerator design, in terms of geometry of the interaction region and conditions of operation. In the following paper, the SVT performance is described. Radiation issues are discussed and the results of different tests aimed to study the decrease in the SVT performance due to radiation damage are presented. The alignment procedure is described, and a few BaBar physics results are presented as examples of the SVT capabilities to reconstruct decay vertices with good resolution and efficiency.