  We explore upper limits for the largest avalanches or catastrophes in
nonlinear energy dissipation systems governed by self-organized criticality
(SOC). We generalize the idealized "straight" power low size distribution and
Pareto distribution functions in order to accomodate for incomplete sampling,
limited instrumental sensitivity, finite system-size effects, "Black-Swan" and
"Dragon-King" extreme events. Our findings are: (i) Solar flares show no finite
system-size limits up to L < 200 Mm, but solar flare durations reveal an upper
flare duration limit of < 6 hrs; (ii) Stellar flares observed with KEPLER
exhibit inertial ranges of $E \approx 10^{34}-10^{37}$ erg, finite system-size
ranges at $E \approx 10^{37}-10^{38}$ erg, and extreme events at $E =(1-5)
\times 10^{38}$ erg; (iii) The maximum flare energy of different spectral-type
stars (M, K, G, F, A, Giants) reveal a positive correlation with the stellar
radius, which indicates a finite system-size limit imposed by the stellar
surface area. Fitting our finite system-size models to terrestrial data sets
(Earth quakes, wildfires, city sizes, blackouts, terrorism, words, surnames,
web-links) yields evidence (in half of the cases) for finite system-size limits
and extreme events, which can be modeled with dual power law size
distributions.
