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We present a catalog of relative proper motions for 368,787 stars in the 30Doradus region of the Large Magellanic Cloud (LMC), based on a dedicatedtwo-epoch survey with the Hubble Space Telescope (HST) and supplemented withproper motions from our pilot archival study. We demonstrate that a relativelyshort epoch difference of 3 years is sufficient to reach a $\sim$0.1 masyr$^{-1}$ level of precision or better. A number of stars have relative propermotions exceeding a 3-sigma error threshold, representing a mixture of MilkyWay denizens and 17 potential LMC runaway stars. Based upon 183 VFTS OB-starswith the best proper motions, we conclude that none of them move faster than$\sim$0.3 mas yr$^{-1}$ in each coordinate -- equivalent to $\sim$70 kms$^{-1}$. Among the remaining 351 VFTS stars with less accurate proper motions,only one candidate OB runaway can be identified. We rule out any OB star in oursample moving at a tangential velocity exceeding $\sim$120 km s$^{-1}$. Themost significant result of this study is finding 10 stars over wide range ofmasses, which appear to be ejected from the massive star cluster R136 in thetangential plane to angular distances from $35^{\prime\prime}$ out to$407^{\prime\prime}$, equivalent to 8-98 pc. The tangential velocities of theserunaways appear to be correlated with apparent magnitude, indicating a possibledependence on the stellar mass.

HST astrometry in the 30 Doradus region: II. Runaway stars from new proper motions in the Large Magellanic Cloud