Zero-shot generalization to unseen embodiments is important for generalizable vision-language-action (VLA) models as robot hardware evolves and task-specific data collection remains costly. However, a systematic understanding of this problem remains limited, in part because the literature lacks a unified zero-shot transfer definition and controlled evaluation settings that isolate embodiment changes from differences in tasks, scenes, or protocols. To address this gap, we first distinguish strict zero-shot transfer, where the target embodiment is absent from all training data, from pretrain-exposed zero-shot transfer, where it appears only during pretraining. We then introduce a controlled benchmark spanning 14 held-out target embodiments across simulation and real-world validation. Within this framework, we conduct a controlled analysis of four factors: state-action representations, pretraining embodiment diversity, auxiliary co-training objectives, and target-embodiment exposure. Experimental results show that local end-effector (EEF) state-action representations, the source embodiment diversity, and auxiliary co-training improve cross-embodiment transfer by around 15, 18, and 7 percentage points, respectively. We further find that adding only 5% target-embodiment data during pretraining improves average target-embodiment progress by 13.4 percentage points, showing that strict and pretrain-exposed zero-shot transfer are distinct and should be reported separately. Together, these findings provide practical guidance for evaluating and improving cross-embodiment VLA transfer in stationary tabletop manipulation with two-finger grippers, while motivating future investigation of broader settings including mobile-base control, dexterous hands, and long-horizon tasks.

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