  Using atomistic simulations we investigate the morphological properties of
graphene deposited on top of a nanostructured substrate. Sinusoidally
corrugated surfaces, steps, elongated trenches, one dimensional and cubic
barriers, spherical bubbles, Gaussian bump and Gaussian depression are
considered as support structures for graphene. The graphene-substrate
interaction is governed by van der Waals forces and the profile of the graphene
layer is determined by minimizing the energy using molecular dynamics
simulations. Based on the obtained optimum configurations, we found that: (i)
for graphene placed over sinusoidally corrugated substrates with corrugation
wave lengths longer than 2\,nm, the graphene sheet follows the substrate
pattern while for supported graphene it is always suspended across the peaks of
the substrate, (ii) the conformation of graphene to the substrate topography is
enhanced when increasing the energy parameter in the van der Waals model, (iii)
the adhesion of graphene into the trenches depends on the width of the trench
and on graphene's orientation, i.e. in contrast to a small width (3 nm)
nanoribbon with armchair edges, the one with zig-zag edges follows the
substrate profile, (iv) atomic scale graphene follows a Gaussian bump substrate
but not the substrate with a Gaussian depression, and (v) the adhesion energy
due to van der Waals interaction varies in the range [0.1-0.4] J/m^2.
