  The spontaneous emergence of scale invariance, called self-organized
criticality (SOC), is often attributed to a second-order absorbing-state phase
transition (ASPT). Many real-world systems display SOC, yet extreme events are
often overrepresented, causing significant disruption, and are called dragon
kings (DK). We show analytically that the tradeoff between driving impulse and
dissipation rate can create DKs in a second-order ASPT. This establishes that
DKs exist in SOC systems, reveals a taxonomy of DKs, and shows that larger
dissipation and smoother driving lower risk of extreme events.
