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This paper presents a complete adaptive finite element-boundary integral (FE-BI) analysis scheme for the time-harmonic, electromagnetic analysis of three-dimensional inhomogeneous scatterers/radiators in free-space. The adaptive scheme is based on an FE-BI formulation which yields electric and magnetic field solutions simultaneously. It employs a posteriori error estimates which exploit the availability of both field solutions and estimates error distributions and global solution quality for the electric and magnetic fields separately. It automatically determines which elements should be refined in order to equi-distribute the estimated error, based on the type of refinement requested (h,p or hp). This automatic determination is based on extrapolating the elemental error estimates. The algorithm terminates when specified tolerance levels are reached by the electric and/or magnetic field global solution quality estimates. The only required user specifications within the algorithm are the termination tolerances and the types of refinements to effect. Results are presented which show that within the scope of the presented error measures significant reductions in computational cost may be achieved. The proposed scheme could be used with other types of error estimates and it could be adapted to other FE or FE-BI formulations.