Wall mounted plumbing fixtures require mounting brackets to be installed within the wall (concealed). The dimensions vary based on the type of bracket, the accessories required, and the model of the carrier. The dimensions below are based on minimum requirements and come from the Plumbing and Drainage Institute. The PDI has a handy PDF chart of space requirements for plumbing fixture supports. Refer to manufacturer information for specific requirements.
Water Closet / Toilet Supports - Adjustable Carriers
Fixed carriers are less common, but require less clear space in the wall cavity.