Using density functional theory methods and large basis sets, we calculated hyperfine coupling constants (HFCCs) for the B-11, O-17, Al-27, and Ga-69 nuclei of the radicals BO, AlO, and GaO (XO), embedded in 2-14 rare gas (Rg) Ne and Ar atoms. Kr atoms were included for AlO. The distance of the Rg atoms from XO was varied from 4 to 12 bohr. Matrix effects cause A(iso)(X) to increase, accompanied by decreases in A(dip)(X) and A(dip)(O), while A(iso)(O) remains close to zero. Changes are largest for AlO, slightly smaller for GaO, and very small for BO, in line with the molecular polarizabilities. Observed changes of A(iso)(X) and A(dip)(X) for BO in Ne matrixes and for AlO in Ne, Ar, and Kr matrixes are reproduced in complexes with 12 Rg atoms at distances of 5-6 bohr or 14 Rg atoms at distances of 6-7 bohr. For GaO, experimental data are available only in Ne matrixes. Theoretical results obtained for HFCCs of O-17 could not be verified due to insufficient experimental information. Estimates of HFCCs in matrixes not yet experimentally studied and for GaO in the gas phase have been made. Due to the interaction with rare gas atoms, p-spin density on the X and O atoms of XO is converted into s-spin density on X, thereby causing an increase (in magnitude) of A(iso)(X), accompanied by decreases in A(dip) of X and O. The higher polarizability of XO along the bond axis is reflected in complexes that have axial Rg atoms showing larger changes in HFCCs than comparable complexes without axial Rg atoms.