  The first complete and explicit SO(1,9) Lorentz descriptions of all component
fields contained in $\mathcal{N} = 1$, $\mathcal{N} = 2$A, and $\mathcal{N} =
2$B unconstrained scalar 10D superfields are presented. These are made possible
by the discovery of the relation of the superfield component expansion as a
consequence of the branching rules of irreducible representations in one
ordinary Lie algebra into one of its Lie subalgebras. Adinkra graphs for ten
dimensional superspaces are defined for the first time, whose nodes depict spin
bundle representations of SO(1,9). An analog of Breitenlohner's approach is
implemented to scan for superfields that contain graviton(s) and gravitino(s),
which are the candidates for the prepotential superfields of 10D off-shell
supergravity theories and separately abelian Yang-Mills theories are similarly
treated. Version three contains additional content, both historical and
conceptual, which broaden the reach of the scan in the 10D Yang-Mills case.
