The recently emerged selective lateral epitaxy of semiconductor planar nanowires (NWs) via the vapor-liquid-solid (VLS) mechanism has redefined the long-standing symbolic image of VLS NW growth. The in-plane geometry and self-aligned nature make these planar NWs completely compatible with large scale manufacturing of NW-based integrated nanoelectronics. Here, we report on the realization of perfectly site-controlled growth of GaAs planar NW arrays with unity yield using lithographically defined gold (Au) seed dots. The growth rate of the planar NWs is found to decrease with the NW width at fixed spacing, which is consistent with the conventional VLS model based on the Gibbs-Thomson effect. It is found that in general, the planar and out-of-plane NW growth modes are both present. The yield of planar NWs decreases as their lateral dimension shrinks, and 100% yield of planar NWs can be achieved at moderate V/III ratios. Based on a study of the shape of seed particles, it is proposed that the adhesion between the liquid-phase seed particle and the substrate surface is important in determining the choice of growth mode. These studies represent advances in the fundamental understanding of the VLS planar NW growth mechanism and in the precise control of the planar NW site, density, width, and length for practical applications. In addition, high quality planar InAs NWs on GaAs (100) substrates is realized, verifying that the planar VLS growth mode can be extended to heteroepitaxy.