Design and characterization of the structural, electronic, and magnetic properties of armchair boron-nitride, BN (BNH), nanosheets were performed by means of density functional theory all-electron calculations. The HSEh1PBE-GGA method together with 6-31G(d) basis sets were used. Non-stoichiometric BNH and BNH compositions: rich in boron or nitrogen atoms, forming homonuclear B or N bonds, respectively, were chosen. The obtained results reveal that these BN nanosheets reach structural stability in the anionic form, where semiconductor and magnetic behaviors are promoted. Effectively, the HOMO-LUMO gap is of 2.03 and 2.39eV, respectively and the magnetic moments are of 1.0 magneton bohrs, coming from the boron atoms in both systems. The rich in boron nanosheets present high-polarity, either in the gas phase or embedded in aqueous mediums like water, as well as low chemical reactivity, signifying potential applicability in the transportation of pharmaceutical species in biological mediums. These systems are also promising for the design of electronic devices, because they possess low-work functions, mainly arising from the homonuclear boron or nitrogen bond formation.