  We show it is consistent with $\ZFC$ that there is an everywhere Kurepa line
which is order isomorphic to all of its dense $\aleph_2$-dense suborders.
Moreover, this Kurepa line does not contain any Aronszajn suborder. We also
show it is consistent with $\ZFC$ that there is a minimal Kurepa line which
does not contain any Aronszajn suborder.
