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Building on results from the Magnetism in Massive Stars (MiMeS) project, thispaper shows how a two-parameter classification of massive-star magnetospheresin terms of the magnetic wind confinement (which sets the Alfv\'en radius RA)and stellar rotation (which sets the Kepler co-rotation radius RK) provides auseful organisation of both observational signatures and theoreticalpredictions. We compile the first comprehensive study of inferred and observedvalues for relevant stellar and magnetic parameters of 64 confirmed magnetic OBstars with Teff > 16 kK. Using these parameters, we locate the stars in themagnetic confinement-rotation diagram, a log-log plot of RK vs. RA. Thisdiagram can be subdivided into regimes of centrifugal magnetospheres (CM), withRA > RK, vs. dynamical magnetospheres (DM), with RK > RA. We show how keyobservational diagnostics, like the presence and characteristics of Halphaemission, depend on a star's position within the diagram, as well as otherparameters, especially the expected wind mass-loss rates. In particular, weidentify two distinct populations of magnetic stars with Halpha emission:namely, slowly rotating O-type stars with narrow emission consistent with a DM,and more rapidly rotating B-type stars with broader emission associated with aCM. For O-type stars, the high mass-loss rates are sufficient to accumulateenough material for line emission even within the relatively short free-falltimescale associated with a DM: this high mass-loss rate also leads to a rapidmagnetic spindown of the stellar rotation. For the B-type stars, the longerconfinement of a CM is required to accumulate sufficient emitting material fromtheir relatively weak winds, which also lead to much longer spindowntimescales. [abbreviated]

A Magnetic Confinement vs. Rotation Classification of Massive-Star Magnetospheres