Using realistic molecular models and accurately calculating the state condition of the fluids of linear and branched alkanes confined between two strongly adsorbing solid surfaces, we obtained strikingly different structure for the two confined fluids. The structure of the n-hexadecane is solid-like with the molecules clearly forming a layered structure. Within each molecular layer, the molecules are packed predominantly parallel to each other. The structures of adjacent layers are correlated such that the main chain axes of the molecules pack into a local hexagonal array. In contrast, the structure of the branched alkane (2,6,11,15-tetramethylhexadecane) fluid remains liquid-like. Although exhibiting density oscillations normal to the confining surfaces, the structure of the confined fluid of the branched alkane is disordered and the molecules are not confined to a particular layer. The amplitude of the density oscillations is much smaller than for the n-hexadecane. The in-plane positional correlation shows isotropic structure characteristic of liquid, and the orientation of the molecules shows very little correlation.