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Depends on budget but the easiest way to do it is IR stripping. Cobra Speedheater is a good one, last time I looked they were around £350. Otherwise there are many methods and you usually need to use a few of them, palm sander can come in handy for small areas at the edges but any sander can bog down with paint, you need to keep them moving to avoid heat building up in the pads and that's not easy in the confined space of a stair tread. A basic carbide scraper can do a lot of work removing layers of paint, a very sharp chisel is useful too.
However you approach it it's one of the worst jobs. Slow, uncomfortable and in the way of the whole household.
Airhead-
Thanks for taking the time for such a full answer, much appreciated.
I think I'll look at painting the "white stripes" either sides of the stair treads a different colour and chose colour and carpet runner carefully.
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I did this, and can confirm it is a complete pain and took much longer than expected. My 1905 house had a thick awful green protective paint under the several layers of white. I heat gunned it (not fancy IR gun just £20 heat gun) and scraped a lot and then sanded a lot. V messy, but looked nice afterwards.
midlife
t.o.
Currently all carpet but they previously had a carpet runner / rods up the middle but there is white paint either side. Thinking about going back to the runner /rods but remove the white paint and stain.