In my experience (limited) with Dalmatian rescue, the old owner has no idea of who the new owner is, just vague details ie.the dog is going to a lovely home with no children, wife works part-time etc etc purely to put the original owners mind at rest. The original owner is also asked to sign a form waiving all rights to the dog.
In Dalmatian rescue, generally, the dog is collected within 24 hours of the initial call, usually by a foster owner or a transporter (they have a network of people across the UK) who will take the dog to his/her new home. They generally have plenty of suitable homes waiting for bitches, so that goes smoothly, its older, uncastrated dogs that they struggle to find experienced homes for.
The majority of calls come because of marital break ups, and, again, come at any time of the day or night.
If a dog is found in rescue then someone is sent to assess to dog, and generally pick him/her up to be fostered until matched with a new home.
Its a dating service for Dalmatians, the owners must be right for the dog :) Thorough homechecks are undertaken, and generally a dalmatian owner will turn up with one of their dogs to see how the potential owner copes with a big spotty hairy loony running all over the place, and jumping on the furniture :)
I guess its easier with Dallies though as they are numerically smaller than Dobes, but they have certainly had their fair share of problems at the hands of a certain set of film makers