The trick here is that the spleen is the enemy of the transfused platelets. In ITP the spleen both makes the antibody against platelets and chews up the antibody-coated platelets. So if you pour platelets into the patient while the spleen is still receiving blood, the spleen simply destroys them and you gain nothing. The natural solution is to wait until the spleen's blood supply is cut. The splenic artery is the dominant feeding vessel, so the moment it is ligated the spleen can no longer filter and destroy circulating platelets. That is the exact window to transfuse: the platelets now survive in the bloodstream and are available to help with clotting during the remainder of the operation. Giving them before incision or at incision wastes them on an active spleen, and waiting until the whole spleen is out is unnecessarily late because the job was already done at artery ligation. Hence platelets are best given right after the splenic artery is tied.\[\boxed{\text{After ligating the splenic artery}}\]