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In this paper, ultra-narrow and highly-efficient straight and Ω-shaped waveguides, and Y-shaped and T-shaped optical power splitters composed of two rows of two-dimensional germanium rods in air are designed and simulated. The position-disordering effect on the waveguides is considered. Finite-difference time-domain numerical simulation results for two rows of straight and Ω-shaped waveguides with no position disordering at the normalized frequency of a λ = 0.327 show optical transmission of 90%, and two rows of Y-shaped and T-shaped power splitters with no position disordering have transmissions >46% for each output branch at the normalized frequency of a λ = 0.327 . Also, the straight and Ω-shaped waveguides with four rows of germanium rods tolerated position disordering of η = 10%. The proposed ultra-narrow waveguides and power splitters are vital components in high-density and all-dielectric optical integrated circuits.