The most common and most likely answer to this crossword clue is the 9 letter word PARENTAGE
I've seen this crossword clue in The Times
P
A
R
E
N
T
A
G
E
Buddy explains!

The straight part
We know that "condition of having children" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case condition of having children = parentage.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does PARENTAGE mean?
PARENTAGE noun- The identity and nature of one's parents, and in particular, the legitimacy of one's birth.
- The social quality of one's class in society.
- Origin; derivation