Who wants what property-wise can play an enormous role in divorce negotiations/proceedings. Sometimes, both spouses will strongly desire to keep a certain piece of marital property. For some types of property, one option that might be available in such a situation is to physically split the property, so each person gets some of it.
Other types of property though generally can't be physically split. Houses fall into this category. However, a new housing design that has come up in Europe seeks to change this.