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Automatic evaluation is an integral aspect of dialogue system research. The traditional reference-based NLG metrics are generally found to be unsuitable for dialogue assessment. Consequently, recent studies have suggested various unique, reference-free neural metrics that better align with human evaluations. Notably among them, large language models (LLMs), particularly the instruction-tuned variants like ChatGPT, are shown to be promising substitutes for human judges. Yet, existing works on utilizing LLMs for automatic dialogue evaluation are limited in their scope in terms of the number of meta-evaluation datasets, mode of evaluation, coverage of LLMs, etc. Hence, it remains inconclusive how effective these LLMs are. To this end, we conduct a comprehensive study on the application of LLMs for automatic dialogue evaluation. Specifically, we analyze the multi-dimensional evaluation capability of 30 recently emerged LLMs at both turn and dialogue levels, using a comprehensive set of 12 meta-evaluation datasets. Additionally, we probe the robustness of the LLMs in handling various adversarial perturbations at both turn and dialogue levels. Finally, we explore how model-level and dimension-level ensembles impact the evaluation performance. All resources are available at https://github.com/e0397123/comp-analysis.