  In this paper, we explore the formation of the marginally trapped and
marginally anti-trapped surfaces that arise from the evolution of homogeneous
dust in D-dimensions with and without the cosmological constant, this is seen
through the analytical expressions for such surfaces. We obtain closed form
expressions for the Norm of the normal to the Horizon that decides their causal
nature and also look at several interesting features of these surface evolution
that are significantly different from the four dimensional counterpart. We
obtain the expressions for the Ashtekar-Badrikrihnan's Area-balance law for
dynamical horizon (spacelike surface) tailored for the case of spherically
symmetric dust evolution in D-dimensions.
