With large language models (LLMs) becoming increasingly prevalent in daily life, so too has the tendency to attribute to them human-like minds and emotions, or anthropomorphize them. Here, we investigate dimensions people use to anthropomorphize and attribute trust toward LLMs across more than 2,000 human-LLM interactions. Participants (N=115) engaged with LLM chatbots systematically varied in warmth (friendliness), competence (capability, coherence), and empathy (cognitive and affective). Warmth and cognitive empathy significantly predicted perceptions on all outcomes (perceived anthropomorphism, trust, similarity, relational closeness, frustration, usefulness), while competence predicted all outcomes except for anthropomorphism. Affective empathy primarily predicted perceived relational measures, but did not predict the epistemic outcomes. Topic sub-analyses showed that more subjective, personally relevant topics (e.g., relationship advice) amplified these effects, producing greater human-likeness and relational connection with the LLM than did objective topics. Together, these findings reveal that warmth, competence, and empathy are key dimensions through which people attribute relational and epistemic perceptions to artificial agents.