The large-scale magnetic field of the Sun, including the open flux that extends into the interplanetary medium, originates in active regions but is redistributed over the photosphere by differential rotation, supergranular convection, and poleward meridional flow. We use simulations to clarify the role of the surface transport processes in the evolution of the total open flux, &PHgr;open, which determines the strength of the radial interplanetary field component. Representing the initial photospheric field configuration by one or more bipolar magnetic regions (BMRs), we show that &PHgr;open varies approximately as the net dipole strength, determined by vectorially summing the dipole moments of the individual BMRs. As meridional flow carries the BMR flux to higher latitudes, the equatorial dipole component is annihilated on a timescale ~1 yr by the combined effect of rotational shearing and supergranular diffusion. The remaining flux becomes concentrated around the poles, and &PHgr;open approaches a limiting value that depends on the axisymmetric dipole strength of the original active regions. We discuss the implications of these results for the solar cycle evolution of &PHgr;open. ¿ 2000 American Geophysical Union