The phrase "assign to" can be replaced with a variety of synonyms to enhance the complexity and sophistication of a piece of writing. Some examples of synonyms for "assign to" include "allocate," "delegate," "designate," "allot," "apportion," "entrust," "design," "decide," "direct," and "appoint." Each of these words adds a unique layer of meaning and implication to the action of assigning something to someone or something else. By using a diverse set of synonyms for "assign to," an author can create variety and depth in their writing, providing a richer, more engaging reading experience for their audience.