I think most of them go to incinerators generally.
I did some math on it a while back, based on the size of the large bins used at my nursery, how many children there are in nappies and how many changes they go through, how full the bins are after a week etc.
Given compression ratios to squash them all down into compact cubes and then stacking these cubes side by side and on top of each other, as well as a rough number and average size of nurseries in my city.
My cities nurseries alone would produce enough compressed blocks of nappies (about 2 foot cubes) to cover a football pitch with layers about 16 foot high in just one year, and that is only the nurseries nappies, not ones used at home or on weekends, nor adult nappies or older children still in them.