We study the single-particle properties of Dirac Fermions confined to a double quantum wire system based on graphene. We map out the spatial regions where electrons in a given subband display the largest occupation probability induced by spatial anisotropic effects associated to the interaction strength between the graphene wires and the substrate. Here, the graphene-substrate interaction is considered as an ad hoc parameter which destroys the zero-gap observed in the relativistic Dirac cone characteristic of graphene electronic energy dispersions. Furthermore, the results indicate that the character of quasi-extended spin states, viewed by multisubband probability density function, is highly sensitive to spatial asymmetries and to the graphene-substrate interaction strength. © 2010 IOP Publishing Ltd.