Large language models now mediate how buyers discover products and services, making the competitive structure of AI-generated recommendations a strategic concern for brands. A basic question has lacked large-scale empirical answers: in a given category, which brand does a model recommend, and how concentrated is that ownership? Across 3,750 responses spanning 50 brands, five industries, and 250 brand-free category queries on three models (GPT-5.2, Google Gemini 3 Flash, and Perplexity sonar-pro), each query repeated five times under a dice-roll stability protocol, we propose three exploratory metrics: the Category Ownership Index (COI), a brand's share of mentions within a category; the Competitive Vacuum Index (CVI), flagging categories with no single leader; and the Displacement Score (DS), quantifying asymmetric substitution between brand pairs. In this sample, recommendation concentration was moderate: the mean Gini coefficient was 0.28 (95% CI [0.16, 0.41]), below the 0.60 power-law threshold we set. Competitive vacuums were rare, appearing in 8.0% of queries, so the models named at least one sampled brand in most cases. Cross-model agreement on the top-recommended brand was 41.6%: a top position on one model did not reliably hold on another. Displacement was industry-dependent, from co-recommendation in consulting (0.4:1) to one-directional substitution up to 4.3:1, with an unweighted mean of 2.4:1 across the five industries. A BERTopic check placed only 4.2% of discovered topic clusters outside the original categories. Within the scope studied, these results sit in tension with a strong winner-takes-all narrative around AI recommendation, and the three metrics offer a candidate, reproducible procedure for competitive-intelligence analysis that future work can validate.

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