Paint spills on porcelain aren't much of a problem. Porcelain resists pretty much any solvent or paint stripping product you throw at it. Moreover, it isn't easily damaged by a paint scraper -- although you wouldn't want to test this by digging the corner of your scraper into the surface -- so you have many options. Even though porcelain is hard, it's always best to start with the least intrusive cleaning method and progress to stronger ones.
Test the Paint First
Before removing hardened paint from any surface, it's important to know whether it's oil- or water-based, so you can use appropriate solvents. The test is simple:
Moisten a rag or cotton swab with denatured alcohol. If you don't have any denatured alcohol around the house, use rubbing alcohol instead.
Rub the paint vigorously for several seconds.
Look at the rag or swab. If color has rubbed off onto it, the paint is water-based. If it's clean, the paint is oil-based.
Rub It Off With a Solvent
Once you determine that the paint is water-based, you can continue rubbing it with the alcohol-soaked rag, wash it with an abrasive sponge and soap and water or use a combination of these methods. Neither alcohol nor water will have much effect if the paint is oil-based, and you may even find mineral spirits ineffective, since this solvent doesn't dissolve cured paint. Instead, rub the spill with a rag dampened with acetone or lacquer thinner. Both of these solvents are flammable and noxious, so wear a respirator; open the windows and avoid open flames.
Use Paint Stripper
Paint stripper removes oil- and water-based paints with equal ease, and it won't damage porcelain. Wear rubber gloves and goggles when using it.
Spread the stripper on the paint with a paintbrush.
Wait about 10 minutes for the paint to start blistering. If that doesn't happen, and the stripper begins to dry out, spread more.
Scrape off the stripper -- and the paint with it -- using a paint scraper. Avoid even the possibility of damage to the porcelain by using a plastic scraper instead of a metal one.
Wash the surface with soapy water after scraping off the paint to clean off residue and neutralize the stripper. Rinse with clear water.
Scrape It Off
In some cases, you may not need stripper or solvent -- thick spots of hardened paint often come off porcelain with just a bit of help from a scraping tool. Wedge the blade of a plastic putty knife between the paint deposit and the porcelain; tap the handle with a hammer; and the paint should fly off into history. If not, give it a little help with lubricating spray. As a last resort, scrape off the paint with a metal putty knife or a razor knife.