We use extensive 3D resistive MHD simulations to study how large-scale current sheets will undergo fast reconnection in the high Lundquist number $S$ limit (above $sim 10^4$), when the system is subject to different externally driven turbulence levels and the self-generated turbulence produced by 3D reconnection dynamics. We find that the normalized global reconnection rate $sim 0.01 - 0.13$, weakly dependent on $S$. Global reconnection with the classic inflow/outflow configurations is observed, and 3D flux ropes are hierarchically formed and ejected from reconnection regions. A statistical separation of the reconnected magnetic field lines follows a super-diffusive behavior, from which the rate is measured to be very similar to that obtained from the mixing of tracer populations. We find that the reconnection rate scales roughly linearly with the turbulence level during the peak of reconnection. This scaling is consistent with the turbulence properties produced by both the externally driven and self-generation processes. These results imply that large-scale thin current sheets tend to undergo rigorous reconnection.
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