Does the solar magnetic flux depends on boundary conditions?

The open flux of the heliosphere is thought to have a floor value during solar minimum. It has been suggested that CMEs increase the total amount of observed flux during solar maximum. This increase is temporary however, presumably due to the fact that CMEs undergo interchange reconnection with the ambient open flux, so that the total open flux of the Sun might be a conserved quantity. We argue that the view on the amount of open flux highly depends on both the inner and outer boundary conditions of the heliospheric system. We demonstrate this argument using a numerical simulation of a real CME event.