There are two specific types of property that come into play, community property and 'joint' owned property. By default and unless there is a premarital agreement, property is deemed 'communal'. That means anything purchased while married, regardless of who purchased it, is deemed to be owned by both parties equally.
In addition there are two types of property, personal property and real estate. Real estate is governed based on where it is located. If the property is in Puerto Rico, under local laws the widower inherits only if there are no descendants (children), ascendants (parents, grandparents and so forth), or side relatives (such as brothers, sisters, nieces, and nephews). Only if none of those exist does the widower or widow inherit existing property IF that property belonged to the spouse prior to marriage. If purchased together until same title, then the widow or widower inherits the whole property. If both are on title but as separate owners, then the spouse inherits 50% (their share, also known as a 'usufruct'), and the other share first goes to descendants, then to ascendants, then to side relatives, and only after all that to surviving spouse. A usufruct is a right to use the products or income from a portion of the estate. Now, this usufruct is also based on how many children may survive. So if for example the widow has 2 children, she inherits 1/3 interest in the usufruct as the other 2/3 goes to the children. To figure out the usufruct a computation must take place which has to consider age and life expectancy of the parties, date of passing, gender of parties, number of other heirs, and percentage of annual revenue.
Hope that helps!