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State-of-the-art automatic speech recognition (ASR) system development is data and computation intensive. The optimal design of deep neural networks (DNNs) for these systems often require expert knowledge and empirical evaluation. In this paper, a range of neural architecture search (NAS) techniques are used to automatically learn two types of hyper-parameters of factored time delay neural networks (TDNN-Fs): i) the left and right splicing context offsets; and ii) the dimensionality of the bottleneck linear projection at each hidden layer. These techniques include the differentiable neural architecture search (DARTS) method integrating architecture learning with lattice-free MMI training; Gumbel-Softmax and pipelined DARTS methods reducing the confusion over candidate architectures and improving the generalization of architecture selection; and Penalized DARTS incorporating resource constraints to balance the trade-off between performance and system complexity. Parameter sharing among TDNN-F architectures allows an efficient search over up to 7^28 different systems. Statistically significant word error rate (WER) reductions of up to 1.2% absolute and relative model size reduction of 31% were obtained over a state-of-the-art 300-hour Switchboard corpus trained baseline LF-MMI TDNN-F system featuring speed perturbation, i-Vector and learning hidden unit contribution (LHUC) based speaker adaptation as well as RNNLM rescoring. Performance contrasts on the same task against recent end-to-end systems reported in the literature suggest the best NAS auto-configured system achieves state-of-the-art WERs of 9.9% and 11.1% on the NIST Hub5' 00 and Rt03s test sets respectively with up to 96% model size reduction. Further analysis using Bayesian learning shows that ...