Collaboratively fine-tuning (FT) large language models (LLMs) over heterogeneous mobile devices fosters immense potential applications of personalized intelligence. However, such a vision faces critical system challenges. Existing federated LLM fine-tuning approaches remain limited by prohibitive on-device resource overhead, straggler-prone synchronous aggregation, and the assumption of a unified pretrained backbone across heterogeneous devices. In this paper, we propose EC-MobiLLM, a novel design for efficient collaborative LLM fine-tuning across heterogeneous mobile devices and heterogeneous backbones. EC-MobiLLM adopts a server-assisted side-tuning paradigm to minimize on-device overhead and pioneers non-blocking asynchronous collaboration to accelerate training. Moreover, EC-MobiLLM introduces adaptive feature alignment to support collaboration across heterogeneous backbones, aligning with practical needs in real-world deployments. Extensive experimental results demonstrate that EC-MobiLLM can maintain robust fine-tuning performance while achieving extremely low on-device memory, with at least 95.2\% reduction in computation overhead, 93.2\% reduction in communication costs and $5.1\times$ faster convergence compared to existing methods, validating its efficacy for practical LLM adaptation over heterogeneous mobile devices.

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