The geometries and stabilization energies (SE) of B3Hn molecules and ions were computed ab initio at MP2-(FULL)/6-31+G* + ZPE(HF/6-3l+C*). QCISD(T)/6-311+G**//MP2(FULL)/6-31+G* (QCI) single point energies and MP2(FC)/6-31+G* analytical frequencies also were calculated for some of these species. The lowest energy isomers of the electron and hydrogen deficient boron hydrides B3H3, B3H4+, B3H4-, B3H5, and B3H6+ have the greatest aromatic stabilization. The aromatic SEs of B3H4-, B3H5, B3H6+, B3H3-2, and B3H3Li2, estimated from appropriate isodesmic equations, approach the large value of the 2 pi-electron cyclopropenium ion. The relative energies and even the character of B3Hn stationary points are influenced strongly by electron correlation. The BE distances vary considerably and depend on the bonding character as well as nonbonded repulsions. The isoelectronic and isostructural analogies between boron and carbon species guide searches for the new boron hydride isomers.