Consider a quiver $Q$ which is not of (euclidean or affine) ADE-type, i.e., $Q$ has wild representation type.
Question: How can I generate an indecomposable $Q$-representation $M$ of arbitrarily large total dimension $\sum_{v\in Q_0}\dim M_v$ over an algebraically closed field?
Such a quiver $Q$ contains a subquiver $Q'$ of affine type ADE (in fact, any connected quiver which is not of Dynkin type contains a subquiver of affine type). Since any representation of $Q'$ can be turned into a representation of $Q$ by putting zero spaces and morphisms on vertices and arrows that don't belong to $Q'$, it suffices to construct representations of arbitrarily large dimensions for $Q'$.
For quivers of affine type ADE, we know how to construct representations of arbitrarily large dimensions; this construction can be found, for instance, in chapter XIII of Elements of the representation theory of associative algebras. Vol. 2, by D.Simson and A.Skowroński.