We study spin transport of holes through microstructures modulated periodically by diluted magnetic semiconductor (DMS) sections, stubless or stubbed. The stubs are symmetric or asymmetric and the magnetizations of consecutive DMS sections are parallel or antiparallel. The transmission coefficients of holes with spin up (T+) or down (T-) are drastically different since the spins feel different potential profiles in the DMS sections. As a result, nearly square-wave patterns, or wide plateaus and oscillations, can be obtained for the transmission and the spin polarization as functions of the incident energy or of various parameters of the periodically repeated unit. Results for simple and composite units with and without deviations from perfect periodicity are reported. Some of the structures considered exhibit a strong spin-filtering behavior. (c) 2005 Elsevier B.V. All rights reserved.