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This paper addresses the issue of automatically generating reduced order models of very large multidimensional systems. To tackle this problem we introduce an efficient parallel projection based model order reduction framework for parameterized linear systems. The underlying methodology is based on an automated multidimensional sample selection procedure that maximizes effectiveness in the generation of the projection basis. The parallel nature of the algorithm is efficiently exploited using both shared and distributed memory architectures. This leads to a highly scalable, automatic, and reliable parallel reduction scheme, able to handle very large systems depending on multiple parameters. In addition, the framework is general enough to provide a good approximation regardless of the model's representation or underlying nature, as will be demonstrated on a variety of benchmark examples. The method provides the potential to tackle, in an automatic fashion, extremely challenging models that would be otherwise difficult to address with existing sequential approaches.