Dad gets torn apart with time — condition of having children (9)
I believe the answer is:
parentage
'condition of having children' is the definition.
(being a parent)
'dad gets torn apart with time' is the wordplay.
'dad' becomes 'pa' (both can mean one's father).
'gets' means one lot of letters go next to another.
'torn apart' becomes 'rent' (past tense of 'rend', to tear or rip).
'with' says to put letters next to each other.
'time' becomes 'age' (an age is a period of time).
'pa'+'rent'+'age'='PARENTAGE'
(Other definitions for parentage that I've seen before include "Who's your father (and mother)?" , "Family origins" , "Ancestors" , "results from birth" , "Extraction, descent" .)