doubt about backend max_connections

Hi all,
I've a doubt about configuring max_pool and num_init_children and,
subsequently, PostgreSQL max_connections.
In <https://www.pgpool.net/docs/46/en/html/runtime-config-connection-pooling.html>
there is this sentence "Please be aware that the number of connections
from Pgpool-II processes to the backends may reach num_init_children *
max_pool in total. " regarding max_pool.
Now, my doubt is: does this apply to all the backends (i.e., every
backend will receive a max_pool * num_init_children connections or
dows it apply "cluster wise", so every node will receive
num_init_childre * max_pool * num_of_backends_in_pgpool?
Seems to me the former, but I want to be sure.

Thansk,
Luca