When some retailers talk about prefinished interior molding, they usually mean polystyrene molding, but wood molding also comes prefinished. Both can split -- although wood is more susceptible to this particular defect -- and the repair is the same for both materials. Splits often happen when you drive a nail into thin material, such as quarter-round molding, and the nail is too close to the edge. You may also have a defective piece of molding -- it happens. You can glue most splits back together, and the best adhesive for the job is good old water-soluble, easy-to-use carpenter's glue.
Remove the nail if the split happened while you were driving one. If you can, take out the rest of the nails and remove the trim, but if that's impractical, shim the split area away from the wall so you can wrap transparent tape around it. If the split trim isn't installed or you're able to remove it, lay it on a flat surface.
Separate the split with a flat-head screwdriver while you dab carpenter's glue onto the wood on both sides of the split with a toothpick.
Close the split and hold it together while you wrap transparent tape around the molding. Pull the tape tight as you're wrapping. Wipe off the glue that oozes out of the split with a damp rag. If the molding isn't installed, you can also use C-clamps to hold the split together.
Let the glue dry overnight, then remove the tape. Sand the repair with 150-grit sandpaper, then touch up the bare wood with wood primer. Apply a coat of paint after the primer dries.