From what I understand, alimony is an antiquated concept that has never been fixed. While the original purpose was for husbands to support home-bound wives who have forsaken careers and need to support themselves, now it basically means that if one partner in a relationship significantly outearns the other, they need to pay alimony to keep the other party in a lifestyle comparable to being married. Child support is factored into alimony, but the purpose is to support the spouse.

Alimony is actually not that easy for a woman to get these days in most states, but in a situation like Castle/Gina where he supported her in a certain lifestyle during the marriage then it is likely she would get it.  It is usually for a set number of years and it always ends when the recipient gets married.  However, since Gina is a high-profile publisher it's hard to say whether she is still receiving alimony. It could be that it was a lump sum payment that she was given.  Also, if she were to marry someone else and then get divorced from that man, Castle would not have to resume his alimony payments.  His obligation ends when she marries someone else, or whenever their divorce decree states that it ends if she never gets married.

Child support, by contrast, is automatic and ends only upon the child reaching the age of majority either by birthdate or emancipation.