  The theory of difference-differential fields of characteristic zero has a
model-companion denoted by $\it DCFA$. Previously we proved a weak version of
Zilber's dichotomy for $\it DCFA$. In this paper we use arc spaces techniques
as developed by Moosa, Pillay and Scanlon to suppress the extra hypothesis
needed before and prove the full Zilber's dichotomy for $\it DCFA$, we also
state how these techniques generalise to partial differential fields with an
automorphism.
