First, a surviving spouse has rights to certain allowances under D.C. law. These get paid off the top regardless of whether there is a valid Will or not.
If the deceased is survived by spouse, children (or grandchildren if one of the children has predeceased) and parents → Spouse takes 2/3 and children split 1/3 (with grandchildren of deceased child sharing in share of his or her deceased parent in equal shares). Surviving parents inherit nothing in D.C. in this situation.
If the deceased is survived by a spouse but no children or grandchildren (of a predeceased child) → Surviving spouse inherits the entire estate.
If no spouse or children or grandchildren survive the decedent → The whole estate is divided equally between the father or mother or the survivor of them.
If no spouse and no parents and no children survive the decedent → Siblings (or descendants of a predeceased sibling) are entitled to the estate. The share of a predeceased sibling with descendants is divided equally among those descendants at the same level.
The surviving grandparents of a decedent inherit only if no "collaterals" survive.
Posthumous children only inherit under certain circumstances outlined in D.C. law.
There is no distinction between whole and half-blood and stepchildren (and thus a stepchild may inherit from a stepparent who dies without a Last Will and Testament or trust).
Learn more about District of Columbia probate law.