Paurotis Palm, Acoelorrphe wrightii
Paurotis palms are constantly growing new shoots and have to be pruned to keep them under control.  Notice the attractive, long, slender trunks.  They are a native of the Everglades.
Click on images to enlarge
The growth habit of the paurotis palm is similar to that of the areca in that a steady supply of new shoots erupt from the base.  In this respect, palm stalks can be selectively left to grow, or removed to reach or maintain a target size.
Alex Driscoll
Certified Arborist #1249A
Plant Guide / Palm Trees / Paurotis