A palm tree is basically a trunk with leaves emerging from that trunk. There can be one or multiple trunks. The leaves or fronds can come off the trunk all the way from the top to the bottom, or just be at the top of the trunk. The leaves are attached to the trunk by a linear stem called the  petiole .Where the petiole attaches to the trunk is called the leaf sheath.. Away from the trunk, the petiole supports leaflets or segments of the leaf.he leaves are attached to the trunk by a linear stem called the  petiole . Where the petiole attaches to the trunk is called the leaf sheath.. Away from the trunk, the petiole supports leaflets or segments of the leaf.