This paper describes the coexisting attractors of parallel connected buck switching converters under a master-slave current sharing scheme. We present the basins of attraction of desired and undesired attractors, which provide design information on the conditions for hot-swap operations. The system employs a typical proportional-integral (PI) controller for regulation. It is shown that the system will converge to different attractors for different initial conditions with the same control parameters. Simulation results are given to illustrate the phenomenon. This study is relevant to practical design. Specifically we show that the stability regions obtained from linear methods (i.e., considering only local stability) can be over-optimistic as the global stability regions are found to be more restrictive in the parameter space.