  Collisionless and weakly collisional plasmas often exhibit non-thermal
quasi-equilibria. Among these quasi-equilibria, distributions with power-law
tails are ubiquitous. It is shown that the statistical-mechanical approach
originally suggested by Lynden-Bell (1967) can easily recover such power-law
tails. Moreover, we show that, despite the apparent diversity of Lynden-Bell
equilibria, a generic form of the equilibrium distribution at high energies is
a `hard' power-law tail $\propto \varepsilon^{-2}$, where $\varepsilon$ is the
particle energy. The shape of the `core' of the distribution, located at low
energies, retains some dependence on the initial condition but it is the tail
(or `halo') that contains most of the energy. Thus, a degree of universality
exists in collisionless plasmas.
