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Cross-domain offline reinforcement learning aims to adapt a policy from a source domain to a target domain using only pre-collected datasets, where environment dynamics may differ. A key challenge is to leverage source data while reducing distributional mismatch, particularly when the target dataset is extremely limited. To address this, we propose Target-aligned Coverage Expansion (TCE), a framework that decides how source data should be used, either by directly incorporating target-near transitions or by expanding state coverage through target-aligned generation, guided by theoretical analysis. TCE builds on a dual score-based generative model to synthesize target-consistent transitions over an expanded state region. Extensive experiments across diverse cross-domain environments show that TCE consistently outperforms state-of-the-art cross-domain offline RL baselines.