Answer: You can harvest the seed pods and grow new Queen Palms without too much difficulty. Seed from green fruits of queen palm (Syagrus romanzoffiana) germinate better than seed from half-ripe or ripe seed so you'll want to collect the seed after they are completely mature but before the pods turn a dark brown and dry.
Palm seeds are enclosed by a fleshy or fibrous fruit wall (mesocarp) that, with few exceptions, must be removed prior to planting. You can cut it away with a knife or you can soak it for several days until it becomes mushy and then you can squeeze the pod to extract the seed. If you decide to soak the pods, soak for 1-7 days, changing the water daily.
Plant your palm seeds in any well draining potting soil or seed starting mixture, burying the seeds twice as deep as the seed is wide. (A half-inch diameter seed should be planted 1 inch deep; a quarter-inch diameter seed should be planted one-half inch deep, etc.) Keep the soil moist but not soggy, keep in a warm location (75-95F) out of direct sunshine, and your seeds will germinate in 3-4 weeks. Best wishes with your new palms!
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