  We empirically verify that the market capitalisations of coins and tokens in
the cryptocurrency universe follow power-law distributions with significantly
different values, with the tail exponent falling between 0.5 and 0.7 for coins,
and between 1.0 and 1.3 for tokens. We provide a rationale for this, based on a
simple proportional growth with birth & death model previously employed to
describe the size distribution of firms, cities, webpages, etc. We empirically
validate the model and its main predictions, in terms of proportional growth
(Gibrat's law) of the coins and tokens. Estimating the main parameters of the
model, the theoretical predictions for the power-law exponents of coin and
token distributions are in remarkable agreement with the empirical estimations,
given the simplicity of the model. Our results clearly characterize coins as
being "entrenched incumbents" and tokens as an "explosive immature ecosystem",
largely due to massive and exuberant Initial Coin Offering activity in the
token space. The theory predicts that the exponent for tokens should converge
to 1 in the future, reflecting a more reasonable rate of new entrants
associated with genuine technological innovations.
