  In models of Asymmetric Dark Matter (ADM) the relic density is set by a
particle asymmetry in an analogous manner to the baryons. Here we explore the
scenario in which ADM decouples from the Standard Model thermal bath during an
early period of matter domination. We first present a model independent
analysis for a generic ADM candidate with s-wave annihilation cross section
with fairly general assumptions regarding the origin of the early matter
dominated period. We contrast our results to those from conventional ADM models
which assume radiation domination during decoupling. Subsequently, we examine
an explicit example of this scenario in the context of an elegant SO(10)
implementation of ADM in which the matter dominated era is due to a long lived
heavy right-handed neutrino. In the concluding remarks we discuss the prospects
for superheavy ADM in this setting.
