Overnight, Daniel's entire life changes when his former lover gives birth to his daughter several months early. Now forced to reevaluate his previously casual relationship with his daughter's mother, he begins to learn the ins and outs of caring for a premature baby with the help of NICU nurse Caroline. But Daniel's initial ambivalence toward parenthood turns into a growing distrust of Caroline's rigid adherence to hospital protocols. Caroline, in return, questions Daniel's fitness as a father and feels as though she's the only one properly advocating for the baby's well-being. tiny father focuses on the tension between parents, healthcare professionals, and the business of hospitals as their priorities overlap, conflict, and come to a head.