A method of forming a three-dimensional object, is carried out by (a) providing a carrier and a build plate, the build plate comprising a semipermeable member, the semipermeable member comprising a build surface with the build surface and the carrier defining a build region therebetween, and with the build surface in fluid communication by way of the semipermeable member with a source of polymerization inhibitor; (b) filling the build region with a polymerizable liquid, the polymerizable liquid contacting the build surface; (c) irradiating the build region through the build plate to produce a solid polymerized region in the build region, while forming or maintaining a liquid film release layer comprised of the polymerizable liquid formed between the solid polymerized region and the build surface, the polymerization of which liquid film is inhibited by the polymerization inhibitor; and (d) advancing the carrier with the polymerized region adhered thereto away from the build surface on the build plate to create a subsequent build region between the polymerized region and the build surface; (e) wherein the carrier has at least one channel formed therein, and the filling step is carried out by passing or forcing the polymerizable liquid into the build region through the at least one channel. Apparatus for carrying out the method is also described