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SUMMARY Lamellar magnetism is a source of remanent magnetization in natural rocks different from common bulk magnetic moments in ferrimagnetic minerals. It has been found to be a source for a wide class of magnetic anomalies with extremely high Koenigsberger ratio. Its physical origin are uncompensated interface moments in contact layers of nanoscale ilmenite lamellae inside an hematite host, which also generate unusual low-temperature (low-T) magnetic properties, such as shifted low-T hysteresis loops due to exchange bias. The atomic-magnetic basis for the exchange bias discovered in the hematite-ilmenite system is explored in a series of papers. In this third article of the series, simple models are developed for lamellae interactions of different structures when samples are either cooled in zero-field, or field-cooled in 5 T to temperatures below the ordering temperature of ilmenite. These models are built on the low-temperature measurements described earlier in Paper II. The important observations include: (i) the effects of lamellar shapes on magnetic coupling, (ii) the high-T acquisition of lamellar magnetism and low-T acquisition of magnetization of ilmenite lamellae, (iii) the intensity of lamellar magnetism and the consequent ilmenite magnetism in populations of randomly oriented crystals, (iv) lattice-preferred orientation of the titanohematite host crystal populations and (v) the effects of magnetic domain walls in the host on hysteresis properties. Based on exemplary growth models of lamellae with different geometries and surface couplings we here provide simple models to assess and explain the different observations listed above. Already the simplified models show that the shapes of the edges of ilmenite lamellae against their hematite hosts can control the degree of low-T coupling between ilmenite, and the lamellar magnetic moments. The models also explain certain features of the low-T exchange bias in the natural samples and emphasize the role of lattice-preferred orientation upon the intensity of remanent magnetization. The inverse link between ilmenite remanence and exchange-bias shift in bimodal low-T ilmenite lamellae is related to different densities of hematite domain walls induced by the clusters of ilmenite lamellae.