Christmas poinsettia, Euphorbia pulcherrima is native to Mexico. Other poinsettias, Euphorbia spp. are native to various parts of the US.
Poinsettias are almost always propagated vegetatively by stem cuttings. However, they certainly can be grown from seed as many new cultivars are developed by cross pollination of existing strains to produce plants with some characteristics from each parent.
Collect the seed pods from your poinsettia plants when they begin to turn brown. Store them in a closed paper bag until the seed pods have completely dried. During this period, the seeds are likely to pop right out of the pods and end up on the bottom of the bag. At that point they are ready to sow.
Poinsettia seeds do not need any special treatment to germinate. Nor do they need light. Sow your seeds, one per small pot, just below the soil surface in evenly moist potting soil. Keep in a warm area of subdued light (no direct sunlight!) and make sure the surface of the soil does not get too dry. In a short time, likely one to two weeks, your poinsettia seeds should germinate and the new seedlings begin to grow. Young seedlings are particularly susceptible to fungal diseases, so make sure there is some air movement around the young plants until they grow several leaves.
While it is possible that you may find a wonderful new cultivar of poinsettia amongst your seedlings, sadly, it is far more likely that the new plants will be quite inferior -- horticulturally speaking -- to either of their parents.
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