There being no reasonable relationship

Question

“There being” is allegedly an absolute phrase. Moreover, because “there being” is the present participle of “there be”, I'd like to learn how to parse/unravel “there be”, to determine/deduce this definition de novo. Please explain the steps or thought process as well, so that I may do this by myself in the future.

For example, this page on absolute phrases says that “an absolute phrase combines a noun. . .”. What's the noun here? Are there any grammatical terms that describe this use of “there”? To what does this “there” refer?

However, [. . .] merely submitting a derogation would not have solved the shortcoming as, in any event, the provisions of the Act were disproportionate, there being no reasonable relationship between the means employed and the aims sought to be pursued by the State.
_{Source: p 60, The English Legal System 2012-2013, Gary Slapper}

Answer 1

The verb is being used here in the sense of exist.

The simple statement would be:

There is a simple relationship.
There is no simple relationship.

Now, if I want to use that statement as a subclause describing a state, I used the present participle:

..., there being a simple relationship.
..., there being no simple relationship.

The thought process is not much different from:

I am walking without an umbrella -> I don't like that it started raining, me walking down the street without an umbrella.
A cat is a predator -> A cat being a predator, you can't stop it from hunting.

Answer 2

An absolute phrase combines a noun and a participle with any accompanying modifiers or objects ...

This is not accurate, even in the terms employed by the author: an absolute clause may in those terms be said to combine an NP and a participle with any accompanying modifiers or objects.

But it is more helpful to think of the absolute construction as a full clause (full in the sense that it includes the verb, its subject and its complements) in which the heading verb is cast as a present participle.

The instance you cite is a participial version of the finite clause there is...; this employs the ordinary 'existential' construction in which there is a 'dummy subject'.