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Rapidly rotating early-type stars with strong magnetic fields frequently showH$\alpha$ emission originating in Centrifugal Magnetospheres (CMs),circumstellar structures in which centrifugal support due to magneticallyenforced corotation of the magnetically confined plasma enables it toaccumulate to high densities. It is not currently known whether the CM plasmaescapes via Centrifugal Breakout (CB), or by an unidentified leakage mechanism.We have conducted the first comprehensive examination of the H$\alpha$ emissionproperties of all stars currently known to display CM-pattern emission. We findthat the onset of emission is dependent primarily on the area of the CM, whichcan be predicted simply by the value $B_{\rm K}$ of the magnetic field at theKepler corotation radius $R_{\rm K}$. Emission strength is strongly sensitiveto both CM area and $B_{\rm K}$. Emission onset and strength are {\em not}dependent on effective temperature, luminosity, or mass-loss rate. Theseresults all favour a CB scenario, however the lack of intrinsic variability inany CM diagnostics indicates that CB must be an essentially continuous process,i.e.\ it effectively acts as a leakage mechanism. We also show that theemission profile shapes are approximately scale-invariant, i.e.\ they arebroadly similar across a wide range of emission strengths and stellarparameters. While the radius of maximum emission correlates closely as expectedto $R_{\rm K}$, it is always larger, contradicting models that predict thatemission should peak at $R_{\rm K}$.

The Magnetic Early B-type Stars IV: Breakout or Leakage? H$\alpha$ emission as a diagnostic of plasma transport in centrifugal magnetospheres