The easiest way to implement this is to have literally everyone pay a flat tax on the non-UBI portion of their income. This then effectively amounts to a progressive income tax on total income. If you do some number crunching, it wouldn't even need to be crazy high to give everyone the equivalent of US minimum wage; comparable to some European countries.
Over time, as more things get automated, you have more people deriving most of their income from UBI, but the remaining people will increasingly be the ones who own the automation and profit from it, so you can keep increasing the tax burden on them as well.
The endpoint is when automation is generating all the wealth in the economy or nearly so, so nobody is working, and UBI simply redistributes the generated wealth from the nominal owners of automation to everyone else. This fiction can be maintained for as long as society entertains silly outdated notions about property rights in a post-scarcity society, but I doubt that would remain the case for long once you have true post-scarcity.
Over time, as more things get automated, you have more people deriving most of their income from UBI, but the remaining people will increasingly be the ones who own the automation and profit from it, so you can keep increasing the tax burden on them as well.
The endpoint is when automation is generating all the wealth in the economy or nearly so, so nobody is working, and UBI simply redistributes the generated wealth from the nominal owners of automation to everyone else. This fiction can be maintained for as long as society entertains silly outdated notions about property rights in a post-scarcity society, but I doubt that would remain the case for long once you have true post-scarcity.