Bathroom Suites Questions?

I have a 1969 house. In the bath, there are white ceramic holders that the towel rack was in. The rack, a piece of plastic-coated wood, was broken. One of the holders or the base it was in is very loose. I would just like to remove them and affix new ones to the wall. It looks like to me they go clear through the wall. How should I remove them? Should I just try to muscle them out or cut more plasterboard wall out around them? I don't know how big they are on other side and don't understand how they are attached. Is there someone that can educate me on this small but very irritating problem?