  This paper considers self-conformal iterated function systems (IFSs) on the
real line whose first level cylinders overlap. In the space of self-conformal
IFSs, we show that generically (in topological sense) if the attractor of such
a system has Hausdorff dimension less than $1$ then it has zero appropriate
dimensional Hausdorff measure and its Assouad dimension is equal to $1$. Our
main contribution is in showing that if the cylinders intersect then the IFS
generically does not satisfy the weak separation property and hence, we may
apply a recent result of Angelevska, K\"aenm\"aki and Troscheit [BLMS, 2020].
This phenomenon holds for transversal families (in particular for the
translation family) typically, in the self-similar case, in both topological
and in measure theoretical sense, and in the more general self-conformal case
in the topological sense.
