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Recently, numerous sparse hardware accelerators for Deep Neural Networks (DNNs), Graph Neural Networks (GNNs), and scientific computing applications have been proposed. A common characteristic among all of these accelerators is that they target tensor algebra (typically matrix multiplications); yet dozens of new accelerators are proposed for every new application. The motivation is that the size and sparsity of the workloads heavily influence which architecture is best for memory and computation efficiency. To satisfy the growing demand of efficient computations across a spectrum of workloads on large data centers, we propose deploying a flexible 'heterogeneous' accelerator, which contains many 'sub-accelerators' (smaller specialized accelerators) working together. To this end, we propose: (1) HARD TACO, a quick and productive C++ to RTL design flow to generate many types of sub-accelerators for sparse and dense computations for fair design-space exploration, (2) AESPA, a heterogeneous sparse accelerator design template constructed with the sub-accelerators generated from HARD TACO, and (3) a suite of scheduling strategies to map tensor kernels onto heterogeneous sparse accelerators with high efficiency and utilization. AESPA with optimized scheduling achieves 1.96X higher performance, and 7.9X better energy-delay product (EDP) than a Homogeneous EIE-like accelerator with our diverse workload suite.