Yes 3 scales Comp A, B or C
Comp A - relative (parent, wife or child) not expected to live or death of wife or child.
Comp B - relative (parent) has died - returning for the funeral / help with affairs / support
Comp C - basically a priority indulgengee - death of grand parent
The Admin world have a table listing most cases and what category the person falls into. Army and RAF follow this but RN are (were) a law unto themselves on this as the ship's Capt could authorise the category.
For a Comp A, no expense is normally spared ie diverting aircraft, helicopter at destination airport for onward travel.
I have seen a Herc taxy into the bay next to a waiting Puma to onmove the Comp A. Another time, a 125 from 32(R) laid on to pick up a wife who was a Comp A, from Gib and fly to Glasgow - that saved 3 hours on the schedule GB / BA flights. In the good old days of Brit Rail, trains could ask Swindon to hold a train for a Comp B who would have missed it otherwise.
It is an excellent system as long as the Comp route is followed. Normally it went wrong when the Admin unit tried to short cut the system. In one case, again in GIb, the RN ship made someone a Comp A without telling anyone in the welfare organisations. It was left to the Regulators to arrange his flight back. There were no seats from Gib for a couple of days so he was left dangling. This depsite having a Movs unit in GIb. Once we heard about the case, a quick phone call to confirm and he was on the next flight from Malaga. Something the Regs didn't know was an option.