  We study the line bundle mean curvature flow on K\"ahler surfaces under the
hypercritical phase and a certain semipositivity condition. We naturally
encounter such a condition when considering the blowup of K\"ahler surfaces. We
show that the flow converges smoothly to a singular solution to the deformed
Hermitian-Yang-Mills equation away from a finite number of curves of negative
self-intersection on the surface. As an application, we obtain a lower bound of
a Kempf-Ness type functional on the space of potential functions satisfying the
hypercritical phase condition.
