  It is shown that path algebras modulo relations of the form $\Lambda = KQ/I$,
where $Q$ is a quiver, $K$ a coefficient field, and $I \subseteq KQ$ the ideal
generated by all paths of a given length, can be readily analyzed
homologically, while displaying a wealth of phenomena. In particular, the
syzygies of their modules, and hence their finitistic dimensions, allow for
smooth descriptions in terms of $Q$ and the Loewy length of $\Lambda$. The same
is true for the distributions of projective dimensions attained on the
irreducible components of the standard parametrizing varieties for the modules
of fixed $K$- dimension.
