Alexander Stephan and other scientists at UCLA argue that they come from comets! More precisely, large icy objects like those in the Kuiper belt of our Solar System, beyond the orbit of Pluto.
But it takes work to explain how so many of these objects hit white dwarfs.
The theory is that these white dwarfs are in binary star systems. When the star that becomes the white dwarf begins to die it emits a lot of gas and loses mass - we know that's how it works. So, the Kuiper belt objects orbiting it start to move further out. There are lots of these things. So, some will interact gravitationally with the other star in binary system and get thrown this way and that... and eventually some will hit the white dwarf!
The scientists did detailed computer simulations to check that this could account for what we see. Even more exciting: sometimes Neptune-like planets will hit the white dwarf! And indeed we see some white dwarfs that have a lot more heavy elements in their atmosphere.
By running large Monte Carlo simulations, Stephan and collaborators demonstrate that this scenario can successfully produce accretion of both Neptune-like planets and Kuiper-belt-analog objects. Their simulation results indicate that ~1% of all white dwarfs should accrete Neptune-like planets, and ~7.5% of all white dwarfs should accrete Kuiper-belt-analog objects.
While these fractions are broadly consistent with observations, it's hard to say with certainty whether this model is correct, as observations are scant. Only ~200 polluted white dwarfs have been observed, and of these, only ~15 have had detailed abundance measurements made. Next steps for understanding white-dwarf pollution certainly must include gathering more observations of polluted white dwarfs and establishing the statistics of what is polluting them.
Also, 7.5% is a lot less than 25%.
I got this from here: