It is well known that graphene grows as flat sheets aligned with the growth substrate. Oriented graphene structures typically normal to the substrate have recently attracted major attention. Most often, the normal orientation is achieved in a plasma-assisted growth and is believed to be due to the plasma-induced in-built electric field, which is usually oriented normal to the substrate. This work focuses on the effect of an in-built electric field on the growth direction, morphology, interconnectedness, structural properties and also the supercapacitor performance of various configurations of graphene structures and reveals the unique dependence of these features on the electric field orientation. It is shown that tilting of growth substrates from parallel to the normal direction with respect to the direction of in-built plasma electric field leads to the morphological transitions from horizontal graphene layers, to oriented individual graphene sheets and then interconnected 3D networks of oriented graphene sheets. The revealed transition of the growth orientation leads to a change in structural properties, wetting nature, types of defect in graphitic structures and also affects their charge storage capacity when used as supercapacitor electrodes. This simple and versatile approach opens new opportunities for the production of potentially large batches of differently oriented and structured graphene sheets in one production run.