  We study the behavior of representation varieties of quivers with relations
under the operation of node splitting. We show how splitting a node gives a
correspondence between certain closed subvarieties of representation varieties
for different algebras, which preserves properties like normality or having
rational singularities. Furthermore, we describe how the defining equations of
such closed subvarieties change under the correspondence. By working in the
"relative setting" (splitting one node at a time), we demonstrate that there
are many non-hereditary algebras whose irreducible components of representation
varieties are all normal with rational singularities. We also obtain explicit
generators of the prime defining ideals of these irreducible components. This
class contains all radical square zero algebras, but also many others, as
illustrated by examples throughout the paper. We also show the above is true
when replacing irreducible components by orbit closures, for a more restrictive
class of algebras. Lastly, we provide applications to decompositions of moduli
spaces of semistable representations of certain algebras.
