Transparent and standardized documentation is essential for building trustworthy generative AI (GAI) systems. However, existing automated methods for generating model and data cards still face three major challenges: (i) static templates, as most systems rely on fixed query templates that cannot adapt to diverse paper structures or evolving documentation requirements; (ii) information scarcity, since web-scale repositories such as Hugging Face often contain incomplete or inconsistent metadata, leading to missing or noisy information; and (iii) lack of benchmarks, as the absence of standardized datasets and evaluation protocols hinders fair and reproducible assessment of documentation quality. To address these limitations, we propose AdaQE-CG, an Adaptive Query Expansion for Card Generation framework that combines dynamic information extraction with cross-card knowledge transfer. Its Intra-Paper Extraction via Context-Aware Query Expansion (IPE-QE) module iteratively refines extraction queries to recover richer and more complete information from scientific papers and repositories, while its Inter-Card Completion using the MetaGAI Pool (ICC-MP) module fills missing fields by transferring semantically relevant content from similar cards in a curated dataset. In addition, we introduce MetaGAI-Bench, the first large-scale, expert-annotated benchmark for evaluating GAI documentation. Comprehensive experiments across five quality dimensions show that AdaQE-CG substantially outperforms existing approaches, exceeds human-authored data cards, and approaches human-level quality for model cards. Code, prompts, and data are publicly available at: https://github.com/haoxuan-unt2024/AdaQE-CG.