Five flare/CME events were selected in this study. One is on May 12, 1997, for which there is only two active regions on the visible solar disc, and the magnetic configuration is rather simple. For other cases, many active regions were visible. They are the flare/CME events that occurred on Bastille Day of 2000, Oct. 28, 2003, Nov. 7, 2004 and Jan. 20, 2005. By tracing the spread of EUV dimming, which was obtained by SOHO/EIT 195 Å fixed-difference images, we studied the CME initiation and development on the solar disc. At the same time we reconstructed the 3D magnetic structure of coronal magnetic fields, extrapolated from the observed photospheric magnetograms by SOHO/MDI. In scrutinizing the EUV brightening and dimming propagation from CME initiation sites to large areas with different magnetic connectivities, we determine the overall coupling and interacting of multiple flux systems in the CME processes. Several typical patterns of magnetic connectivity are described and discussed in the view of CME initiation mechanism or mechanisms.