We use resistive magnetohydrodynamics (MHD) simulations to investigate the generation and topology of flux transfer events (FTEs) at Earth's dayside magnetopause under generic southward interplanetary magnetic field (IMF) conditions. We focus on three questions: (1) Can FTEs form spontaneously under steady solar wind conditions? (2) What is the role of magnetic reconnection in the generation of FTEs? (3) What effect do FTEs have on the magnetopause magnetic field topology? We find that in the simulations, FTEs form spontaneously under steady solar wind conditions. In contrast to the multiple X line model of Raeder (2006), dipole tilt is not required to produce FTEs in resistive MHD simulations. Further, FTEs are generated by flow vortices which begin to grow well before magnetic reconnection changes the magnetopause magnetic field topology. FTEs form under steady southward IMF conditions but not under steady northward IMF conditions, suggesting that the magnetopause becomes unstable when the IMF turns southward. In our simulations, this instability appears to be triggered by a movement of the flow stagnation point away from the magnetic separator, which modifies the subsolar stagnation point flow, thereby rendering it unstable. Finally, examination of the internal magnetic structure of the simulated FTEs reveals a complex topology resulting from multiple separator bifurcations driven by plasma flows within the FTEs.