I was told that the fertilzer U may use for your lawn should not be put too close the palm roots which go out to the drip line.
Therefore, the beds around the palms should be large as the drip lines.
If you don’t know what the drip line is, its the area on the outer edge of the canopy where the majority of water runs off of the tree and falls to the ground. This is where the majority of your water absorbing roots are, not near the trunk, where people most commonly water. It is also important to have your drip system here as well.