DNS update question

[Tester]

Hi there,
What happens if someone changes domain/IP address and some dns servers from
the internet give still the old IP/domain name and some the new ip/domain
name? How long does it take to propagate? I guess if I try accessing by new
IP address it will route OK over the internet(instead of using the name).
How could I refresh my dns server cache fom the "updated" root servers? It
is not my domain/IP, it is one of our partners'.
Thanks a lot, Calin