Whose line is it anyway?

[Officially Retired]

I've often heard people refer to a certain guy's dogs as his line. It's often referring to someone who doesn't really have a line, yet has had or still has notable dogs.
There are, however, still people who have cultivated active lines, still winning their share and thriving in one way or another. This is what brings me to my question.
Starting with the very beginning someone puts those first two dogs together that he likes and breeds, when is it his or her lineage?
We'll call a guy Joe Blow. He acquires two dogs, likes them and breeds them together. His litter is called what? They are Joe Blow's dogs, but are they Joe Blow dogs by lineage? What do you call them, and when do you acknowledge them as Joe Blow dogs and not just dogs that belong to Joe Blow?
Is it accomplishment? After all, people have bred a continuum of not-so-good dogs for many generations and just kept the lineage going anyway.
I'm not asking where you think the "origin" of his line is. That's obvious, I think. It's those first two dogs. I AM asking when you begin calling them the Joe Blow line. I'm interested to hear your reasons, also.

It is my belief that "a line" starts when someone intends it to start.

By that I mean, if a guy decides in his mind that "this dog" is worthy of building a line on, and he makes breedings with the intent to build a line on that dog, then a line is being developed. This is in stark contrast to a man who breeds two dogs together to "get pups." The truth is, most people "breed two dogs together," with absolutely zero intent of building a bloodline on any particular dog.

Therefore, a bloodline begins when a man (or woman) decides to build one, and makes their breeding choices with that specific purpose in mind, which is to duplicate and preserve the (hopefully) outstanding traits of some stand-out dog.

Jack