Conventional pick-and-place technology platform in handling microscale component assembly processes has technical limitations in terms of capacity, efficiency, and accuracy. The fluidic self-assembly (FSA) approach employs a lubricant fluid carrying micropart flows over a target wafer patterned with binding sites, which results in part-substrate attachment. This technique transports microparts from one location to another with orientation control and parallel sorting. The present study demonstrates a FSA approach for fast, economic, and precise handling of microscale parts with square (few are in rectangular) shapes. The microparts fabricated from silicon-oxide wafers and ranging in size from aligned and filled to designated sites in the substrate under water. The effects of micropart sizes and lubricants on the FSA processes are compared. This study provides a fundamental analysis for achieving and optimizing the self-alignment. The polymer or solder adhesion force of the square-patterned micropart immobilized at the larger binding sites were estimated to be and , respectively, which results in higher assembly yield of up to 100% for these samples.