The size, shape and distribution of InAs quantum dots (QDs) grown on cross-hatch InGaAs virtual substrates via molecular beam epitaxy (MBE) are investigated by systematic variations in the degree of QD overgrowth, QD growth rate and GaAs capping layer thickness. It is found that increasing overgrowth and/or growth rate, in combination with migration-enhanced epitaxy, results in the formation of uniform, high-density QDs where preferential alignment along the two orthogonal cross-hatch directions, [110] and [1-10], is maintained. Capping of QD hatch results in asymmetrical shape transformation where quantum dashes along [110] direction and wires along [1-10] can be formed on the same substrate in one continuous MBE process. The various shapes, sizes, and distributions of QD hatches provide means for engineering of optoelectronic devices