The method of Wallpaper border removal depends on what the Border was applied on, like painted wall or not, was it applied over wallpaper, and what was used to hang the wallpaper border. If it's on wallpaper, it can be easily peeled off. However, if it's on a painted wall, dampening the lower layer with warm water, and letting it soak for a while considerably make the job easier.
You can use any commercial chemical wallpaper remover if the border is a genuine Wallpaper border and is reasonably new. The remover will reactivate the adhesive and let you scrape off the paper with a scraping tool. However the chemical usually won't permeate if the wallpaper border has a vinyl outer covering. Use a perforation tool to break the surface so the moisture can reach the adhesive.
Peel the wallpaper border with soft metal or plastic scraper, and not tools like strong metal scrapers or filling knives, which may result in unwanted scratches on the wall. If the Wallpaper border material is fibrous, like paper, you can use a garden sprayer to drench it with the chemical remover, and then remove the remaining residue. Use a wallpaper steamer to reactivate the paste. You can then easily scrape of the paper.
You can also use steam removal method for Wallpaper borders. First, steam the surface of the wall. Start from the bottom to the topmost part, one section at a time. If the wallpaper border uses extremely strong adhesive, you may need to steam each strip twice or thrice before removing. Use a broad knife to scrape a strip of wallpaper off the wall, working from the bottom up. And while the adhesive is still warm, scrape each strip of paper. Using warm water and sponge, remove remaining adhesive residue.