Using numerical micromagnetics we have studied the ground state magnetization distribution of square planar ferromagnetic elements (“nanostructures”). As the element size is reduced from 250 to 2 nm at constant thickness (2–35 nm), we find that the magnetization distribution undergoes up tothreephase transitions involving as many as three different near single domain states. One of these phase transitions is analogous to the reorientation phase transition observed in continuous ultrathin magnetic films. ©1998 American Institute of Physics.