  The goals of this article are as follows: (1) To determine the irreducible
components of the affine varieties parametrizing the representations of $
\Lambda $ with dimension vector d, where $ \Lambda $ traces a major class of
finite dimensional algebras; (2) To generically describe the representations
encoded by the components. The target class consists of those truncated path
algebras $ \Lambda $ over an algebraically closed field K which are based on a
quiver Q without oriented cycles. The main result characterizes the irreducible
components of the representation variety in representation-theoretic terms and
provides a means of listing them from quiver and Loewy length of $ \Lambda $.
Combined with existing theory, this classification moreover yields an array of
generic features of the modules parametrized by the components, such as generic
minimal projective presentations, generic sub- and quotient modules, etc. Our
second principal result pins down the generic socle series of the modules in
the components; it does so for more general $ \Lambda $, in fact.
  The information on truncated path algebras of acyclic quivers supplements the
theory available in the special case where $ \Lambda = KQ $, filling in generic
data on the d-dimensional representations of Q with any fixed Loewy length.
