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Heterogeneous Large Language Model (LLM) fusion integrates the strengths of multiple source LLMs with different architectures into a target LLM with low computational overhead. While promising, existing methods suffer from two major limitations: 1) **reliance on real data from limited domain** for knowledge fusion, preventing the target LLM from fully acquiring knowledge across diverse domains, and 2) **fixed data allocation proportions** across domains, failing to dynamically adjust according to the target LLM's varying capabilities across domains, leading to a capability imbalance. To overcome these limitations, we propose Bohdi, a synthetic-data-only heterogeneous LLM fusion framework. Through the organization of knowledge domains into a hierarchical tree structure, Bohdi enables automatic domain exploration and multi-domain data generation through multi-model collaboration, thereby comprehensively extracting knowledge from source LLMs. By formalizing domain expansion and data sampling proportion allocation on the knowledge tree as a Hierarchical Multi-Armed Bandit problem, Bohdi leverages the designed DynaBranches mechanism to adaptively adjust sampling proportions based on the target LLM's performance feedback across domains. Integrated with our proposed Introspection-Rebirth (IR) mechanism, DynaBranches dynamically tracks capability shifts during target LLM's updates via Sliding Window Binomial Likelihood Ratio Testing (SWBLRT), further enhancing its online adaptation capability. Comparative experimental results on a comprehensive suite of benchmarks demonstrate that Bohdi significantly outperforms existing baselines on multiple target LLMs, exhibits higher data efficiency, and virtually eliminates the imbalance in the target LLM's capabilities.