Answer: Your tree will produce splits or fissures in the bark if it is under strees, especially from over-watering or poorly draining soil. There's not much you can do to stop the sap from flowing other than correct the condition that caused the splits. Once you adjust your watering or fix the drainage, the trunk should heal itself and stop oozing sap. The new growth you see at the base are called suckers - they grow from the roots of Brazilian Pepper Trees. Keep them cut down to maintain a single trunked tree. If you allow the suckers to grow, they will eventually become trees and colonize the entire area with many pepper trees.
Best wishes with your pepper tree!
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