  This work provides complete description of Quasistationary Distributions
(QSDs) for Markov chains with a unique absorbing state and an irreducible set
of non-absorbing states. As is well-known, every QSD has an associated
absorption parameter describing the exponential tail of the absorption time
under the law of the process with the QSD as the initial distribution. The
analysis associated with the existence and representation of QSDs corresponding
to a given parameter is according to whether the moment generating function of
the absorption time starting from any non-absorbing state evaluated at the
parameter is finite or infinite, the finite or infinite moment generating
function regimes, respectively. For parameters in the finite regime, it is
shown that when exist, all QSDs are in the convex cone of a Martin entry
boundary associated with the parameter. The infinite regime corresponds to at
most one parameter value and at most one QSD. In this regime, when a QSD
exists, it is unique and can be represented by a renewal-type formula. Multiple
applications to the findings are presented, including revisiting some of the
main classical results in the area.
