The goal of this paper is to examine various interpretations of the notion of 'parallel function' in pronoun assignment. The term usually denotes a strategy of assigning an ambiguous pronoun to an antecedent which has the same grammatical role (e.g., subject, object, etc.). However, I will show that the pronoun's grammatical and thematic roles both influence assignment; that differences in clausal attachment and global constituent structure can reduce the proportion of syntactically parallel assignment, consistent with a priming model of the comprehension of multiclause sentences; and that subject pronouns are very strongly biased toward subject assignment because the preceding clause always has a parallel subject NP, and because assignment begins before information (either supporting or contradictory) about the pronoun's thematic role becomes available to the processor. Implications for Al and for language acquisition are also discussed.