European Fan Palm, Chamaerops humilis
This is the choice for a tiny palm tree.  They are usually found around three feet tall.  If you do find a tall one, it is quite valuable.  They are a slow growing, low maintenance palm.
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This tropical arrangement includes a European fan palm in front with pygmy date, cardboard plant, sylvester and lady palms as a backdrop.
Alex Driscoll
Certified Arborist #1249A
Plant Guide / Palm Trees / European Fan