Inter-Site Topology Generator (ISTG).

Hi,
I have recently moved roles from a domain controller to another.
I’m going to remove the first one from the network but before that I want to be sure that I won’t have problems afterwards
The new one seems to work very fine.
The problem is that the one I want to remove is still acting as the Inter-Site Topology Generator.
I can see that in the NTDS site settings.
Is the new domain controller going to take ownership of the role after demoting the other one? because I tried to change itmanually but I was not able.
Tanks.