Quantum transport effects in various nanosized graphite sheets are studied on the basis of the Landauer model. To derive heteroatomic effects in quantum transport, nanosized graphite sheets that involve B, N, and O atoms are treated. Important rules for effective quantum transport are found: (I) two atoms connected with metallic leads should have large molecular orbital (MO) coefficients in the frontier orbitals (i.e., the highest occupied MO (HOMO) and the lowest unoccupied MO (LUMO) or other MOs in the vicinity of the Fermi energy); (II) the product of MO coefficients at the two atoms should be different in sign between the HOMO and LUMO, and the product of MO coefficients at the two atoms should be same in sign between the HOMO (LUMO) and other occupied (unoccupied) orbitals near the Fermi energy. Heteroatoms are useful to enhance quantum transport effects because heteroatoms in nanosized graphite sheets can decrease the energy gaps and localize the T-electronic populations at certain sites in the HOMO and LUMO.