An offset umbrella base needs to be very stable and strong to support the off-center weight and wind load of an offset market umbrella. Having a substantial footprint in combination with substantial weight leads to a stable base. Below is an example of such an offset stand. Clicking on the image will take you to amazon where the item can be purchased.
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Sometimes one prefers the style of a more standard market umbrella base. These sort of bases can sometimes be used as an offset umbrella base if selected carefully for weight and stability, and depending on the size and weight of the offset umbrella itself.