We have used a magnetic accretion model to investigate the accretion flows of magnetic cataclysmic variables (mCVs) throughout a range of parameter space. The results of our numerical simulations demonstrate that broadly four types of flow are possible: discs, streams, rings and propellers. We show that the equilibrium spin periods in asynchronous mCVs, for a given orbital period and magnetic moment, occur where the flow changes from a type characterised by spin-up (i.e. disc or stream) to one characterised by spin-down (i.e. propeller or ring). 'Triple points' occur in the plane of spin-to-orbital period ratio versus magnetic moment, at which stream-disc-propeller flows or stream-ring-propeller flows can co-exist. The first of these is identified as corresponding to when the corotation radius is equal to the circularisation radius, and the second as where the corotation radius is equal to the distance from white dwarf to the L1 point. If mCVs are accreting at their equilibrium spin rates, then for a mass ratio of 0.5, those with Pspin/Porb < 0.1 will be disc-like, those with 0.1 < Pspin/Porb < 0.5 will be stream-like, and those with Pspin/Porb ~ 0.5 will be ring-like. In each case, some material is also lost from the binary in order to maintain angular momentum balance. The spin to orbital period ratio at which the systems transition between these flow types decreases as the mass ratio of the stellar components increases, and vice versa
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