In this work, we report the controlled growth of one-dimensional (1D) and two-dimensional uniform, well-arranged self-assembled Ge dots grown on patterned Si (0 0 1) substrates. Selectively epitaxial growth (SEG) of Si mesas was first performed in an MBE system equipped with a gas sourer of Si2H6 and a Knudsen cell of Gs. Self-assembled Ge dots on one-dimensional Si SEG stripe mesas demonstrate the periodic arrangement with uniform size, which is different from the bi-modal distribution as normally seen. This cooperative arrangement is attributed to the nature of self-regulation of the self-assembled system with the assistance of the spatial confinement. A systematic study of the one-dimensional arrangement M:ill be discussed. The atomic force microscopic results of two-dimensional arrays show that there are several kinds of the arrangement configurations, indicating the possibility of the controlling the placement of self-assembled Ge dots. Finally, we will discuss the mechanisms of the cooperative arrangements and the possibility to control freely spontaneous growth of Ge dots on pre-grown Si mesas.