I have a son. My cousin (my father’s, brother’s son) has a son. What is my son and his son’s relationship title?
they are cousins, once removed.
Your first cousin is your son’s first cousin once removed. Your son and your cousin’s son are second cousins.
They are second cousins.
Your relationship to your cousin’s son is first cousin once removed. The once indicates one generation.
If your son and your cousin’s son have children those children will be third cousins.
second cousins
his son is your first cousin once removed. Here’s how it works and why JPL is wrong. Think of your family tree with each generation as a level. If cousins are on he same level, look back to find your first common ancestor. Grandparents = first cousins, Great-Grandparents = second cousins, Great-Great-Grandparents = third cousin, etc.
If they are not on the same level, look back starting at the level of the oldest generation. Then each level of difference is one level removed. For example, start with your second cousin i.e. common great-grandparents.
Your second cousin’s child is your second cousin once removed.
Your second cousin’s grandchild is your second cousin twice removed.
Your second cousin’s great-grandchild is your second cousin thrice removed.
Your second cousin’s child and your child are third cousins.
Your second cousin’s grandchild and your child are third cousins once removed.
etc.
Second cousins. They are in the same generation as each other, but one generation away from being first cousins.
How does the “removed” work again?
Specifically: My mom’s cousin. I understand her children are my second cousins. But my mom’s cousin herself, is she my second cousin once removed, or first cousin once removed? Or is it ambiguous and can go either way?
First cousin once removed. No ambiguity.
Unlike other asymmetric relations (you are your nephew’s uncle, your grandparent’s grandchild) you are your 1st cousin 1x removed’s … 1st cousin 1x removed.
In other words your first cousin 1x removed can be one generation earlier than you (your parent’s 1st cousin) or one generation after you (your cousin’s child). Similarly “two times removed” will be off by two generations, in either direction.
Most rigorous, if too pedantic, is to locate the common ancestor(s) and count generations. For example if your gt-gt-gt-gt grandparents are same as target’s gt grandparents, then you are 2nd cousins 3x removed.
As noted, it’s not ambiguous at all following the ‘rules’ of cousinry. Having said that, it is (or at least, was) not unusual at all to hear older folks referring to a “first cousin once removed” as “second cousin.” So I wonder how they would have referred to true second cousins.
Well, the n[sup]th[/sup] cousin, m times removed nomenclature is ambiguous, in the sense that the relationship is asymmetric, as septimus notes above, yet we use the same phrase to describe each one’s relation to the other.
ETA: So, my “first cousin once removed” could be either my first cousin’s child, or could be my parent’s first cousin.
I have a 0[sup]th[/sup] cousin who has mentioned several times that there exists another distinct system of nomenclature to describe cousin relationships, but he didn’t know what that method is. Does anyone here know of that?
0th cousin?? 
Are y’all double first cousins or something? I think they are as close as siblings.
Actually, in this system, the definitions for cousins are symmetric - you are your first cousin once removed’s first cousin once removed, just as you are the sibling of your sibling. An asymmetric definition is used for uncle and niece.
It’s no more ambiguous than calling someone your first cousin, regardless of whether they’re your mother’s brother’s daughter, or your father’s sister’s son, or you mother’s sister’s daughter, or your father’s brother’s son, etc., etc., etc.
You can call eight people your first cousin, yet each is related to you differently.
To clarify this, I think Senegoid means he and his informant share two (minus 1st) half-cousins 1x removed. 
The Catholic church uses a terminology in deciding whether a couple is too consanguinous for marriage.
They are second cousins.
However, Catholic rules on consanguinity are irrelevant because the OP specified that both children are sons and the Catholic Church does not recognize gay marriage at all, let alone gay cousin marriage.
Read my post above.
Removed refers to how many generations there are between the two. So for example, the grandchild of your third cousin and you are third cousins twice removed.
[QUOTE=septimus]
In other words your first cousin 1x removed can be one generation earlier than you (your parent’s 1st cousin) or one generation after you (your cousin’s child). Similarly “two times removed” will be off by two generations, in either direction.
[/QUOTE]
[QUOTE=Senegoid]
Well, the nth cousin, m times removed nomenclature is ambiguous, in the sense that the relationship is asymmetric, as septimus notes above, yet we use the same phrase to describe each one’s relation to the other.
[/QUOTE]
You are both incorrect as the “cousin” relationship refers to the earlier generation. Let’s take as an example second cousins. You claim that you would be second cousins once removed from both ther child and parent. But that’s not true, you are a first cousin once removed from the parent. Why? Because your parent and their parent are first cousins. You are one generation YOUNGER removed from that relationship and so you and your second cousin’s parent are first cousins once removed. The asymmetry comes from the fact that the relationship is always described from the perspective of the older generation and never the younger.
I have multiple personality disorder and so do I.
Aren’t there theories that due to pedigree collapse, on average everyone is at least 50th (or some other number) cousin to everyone else?
Slight hijack:
The linked-to version of the Catholic Encyclopedia is from 1913. Do not rely on the “New Advent” site if you need information on the current state of the canon law (or anything else Church-ly).
Why 1913? It is out of copyright, so post-able:
That’d be siblings. -1st cousin is just yourself. -2nd cousin are a couple with children. -3rd are grandparents, etc.