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Adenium obesum, as recognized here, occurs in two disjunct populations. One occurs nearly all the way across Africa in a broad band south of the Sahara, from Senegal to Sudan and Kenya. Another population, supposedly of the same species, occurs in Tanzania, southern Kenya, and northern Mozambique. In any case, neither of these can properly be called A. obesum if one recognizes more than one species. That's because the type specimen of this species is from Aden on the Arabian peninsula. The plants we call A. arabicum are in fact the true A. obesum.
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Growing this rare tropical plant in my indoor garden in Chicago has been a big learning experience. When I started hanging around gardening forums and reading about this plant I came across many threads and people that commented on how hard it was to keep this plant alive and healthy. Many people discouraged this plant for beginners to container gardening or for people who don't have don't have a greenhouse or windows that receive full sun.
In the spring and summer I put my plants outdoors and sit them among the other plants in my container garden. Since I'm gardening in a small space and the plants are rather small I place the pots on top of a larger pot. They're heat tolerant plants and like a lot of sun and because of that they get a generous amount of water in the summer whenever I'm watering.
They stay in my outdoor garden among my flowers and other plants but in the fall they start to prepare to be brought into my indoor garden. I don't have plant lights or an indoor plant light set up so they have to make due with sitting in a west facing window. By the time they're brought it they have lost all of their leaves because of the cooler weather and are pretty much dormant. I allow them to go dormant because I don't have grow lights for them and I find it's just easier not to worry about one more plant. During the Adenium Obesum's dormancy I don't water much or any if I can help it because if I did it would spring back to life. The slightest amount of water that I give them after they've been brought in for the winter will start the plant up again. I allow them to get so dry that the caudex ( the trunk) starts to shrink but even then I'll hold back the water.
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Sources: Wikipedia, Wikimedia, Prota4u, Tucsoncactus, Mrbrownthumb