If he happens to come, I want you to hand him these documents.

Literal

By-chance he [subject-が] come-[conditional-たら], this document [object-を] hand-over-want [てほしい].

渡してほしい ('want you to hand over') uses the third-person desire construction ~てほしい. The agent (who should do the handing) is unspecified but clearly the addressee. Compare the first-person ~たい ('I want to') — both are desire forms but differ in whose action is desired.