Epitaxially aligned large silver (Ag) nanoplate arrays with ultraclean surfaces are very attractive for novel plasmonic applications. Although solution-phase methods have been extensively employed to synthesize Ag nanoplates, these cannot be used to grow epitaxial large Ag nanoplates on substrates. Here we report a vapor-phase synthetic strategy to epitaxially grow submillimeter-scale Ag nanoplates on a variety of substrates. By simply transporting Ag vapor to the substrates at an optimal temperature (820 degrees C), we synthesize similar to 100 mu m-sized Ag nanoplates with atomically clean surfaces, which are three-dimensionally aligned on the substrates. We demonstrate that both the type of supported seed and their interfacial lattice matching with the substrates determine the epitaxial growth habit of the nanoplates, directing their crystallinity, shape, and orientation. (i) On r-cut sapphire substrates, twinned pentagonal nanoplates grow vertically from twinned triangular seeds through a seed -> nanoplate process. (ii) On m-cut sapphire substrates, twinned trapezoidal Ag nanoplates grow slantingly from twinned decahedral seeds through a seed -> NW -> nanoplate process. (iii) Interestingly, twin-free single-crystalline trapezoidal Ag nanoplates grow from twin-free square pyramidal seeds on STO (001) substrates through a seed -> NW -> nanoplate process. The epitaxially aligned Ag nanoplate arrays could serve as a new platform for two-dimensional (2D) guiding of surface plasmons as well as for hierarchical 3D plasmonic nanoarchitecturing.