There are several synonyms for the phrase "support publication." One common synonym is "back publication," which means to financially or morally support the production and distribution of written works. Another synonym is "endorse publication," which conveys a similar message of approval or public promotion. "Champion publication" suggests a more active and passionate form of support, involving advocacy and defense of a particular publication or author. "Sponsor publication" implies a financial investment in the production process, while "encourage publication" emphasizes the positive impact that publishing can have on authors and readers alike. Overall, these synonyms all convey the central idea of providing support and encouragement for the creation and dissemination of written works.