I noticed the other day that the tile on my bathroom wall is falling apart. It looks like that its on a plasterboard. Does anyone have any suggestions?

I'm not quite sure what your question is. Are you wanting to remove the remaining tiles from the wall? Or, are you wanting to re-attach tiles that are falling off the wall?

At any rate, have the tiles been "falling apart" for a long time? Or, is this something that has just started to happen recently?

The short answer is remove the tile, old plaster and start over. Any cracks either in tile or joints where water can get into only leads to more problems later on. Caulk is not a permanent fix. Spend the money, do it right and enjoy life for a long time.