  We investigate the delocalization transition appearing in an exclusion
process with two internal states resp. on two parallel lanes. At the
transition, delocalized domain walls form in the density profiles of both
internal states, in agreement with a mean-field approach. Remarkably, the
topology of the system's phase diagram allows for the delocalization of a
(localized) domain wall when approaching the transition. We quantify the domain
wall's delocalization close to the transition by analytic results obtained
within the framework of the domain wall picture. Power-law dependences of the
domain wall width on the distance to the delocalization transition as well as
on the system size are uncovered, they agree with numerical results.
