The most common and most likely answer to this crossword clue is the 13 letter word BRAINCHILDREN
I've seen this crossword clue in The Sunday Telegraph
B
R
A
I
N
C
H
I
L
D
R
E
N
More clues leading to the result BRAINCHILDREN
Buddy explains!
The straight part
We know that "Products of a fertile imagination?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case products of a fertile imagination? = brainchildren.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 BRAINCHILDREN mean?
BRAINCHILDREN noun- A creation, original idea, or innovation, usually used to indicate the originators