  A generalized theory of the self-limiting assembly of twisted bundles of
filaments and columns is presented. Bundles and fibers form in a broad variety
of supramolecular systems, from biological to synthetic materials. A
widely-invoked mechanism to explain their finite diameter relies on chirality
transfer from the molecular constituents to collective twist of the assembly,
the effect of which frustrates the lateral assembly and can select equilibrium,
finite diameters of bundles. In this article, the thermodynamics of
twisted-bundle assembly is analyzed to understand if chirality transfer is
necessary for self-limitation, or instead, if spontaneously-twisting, achiral
bundles also exhibit self-limited assembly. A generalized description is
invoked for the elastic costs imposed by twist for bundles of various states of
intra-bundle order from nematic to crystalline, as well as a generic mechanism
for generating twist, classified both by {\it chirality} but also the {\it
twist susceptibility} of inter-filament alignment. The theory provides a
comprehensive set of predictions for the equilibrium twist and size of bundles
as a function of surface energy as well as chirality, twist susceptibility, and
elasticity of bundles. Moreover, it shows that while spontaneous twist can lead
to self-limitation, assembly of twisted {\it achiral} bundles can be
distinguished qualitatively in terms of their range of equilibrium sizes and
thermodynamic stability relative to bulk (untwisted) states.
