A memory system for digital data communication with a host device is described to provide data storage capacity. The system can include a controller and a plurality of modules, each module including a nonvolatile memory device wherein the module is configured to perform a management function with respect to the module at least partially based on a parameter. The parameter is provided by the controller and/or the module. The system and modules, in one feature, can support multiple forms of concurrency with respect to data accesses involving the modules.