The phrase "a vast relationship" is correct and usable in written English.
It can be used to describe a relationship that is extensive or significant in scope, depth, or complexity.
Example: "Their collaboration led to a vast relationship that spanned multiple industries and countries."
Alternatives: "a broad relationship" or "an extensive relationship".
The entire cosmos was conceived as a vast network of relationships, each component of which, whether divine or human, must know its place and fulfill its appointed role.
To be more concrete, let me say the following: There is a vast literature about the relationship between culture, entrepreneurship and economic growth (Doepke and Zilibotti 2014).
With Pushkin as his inspiration, Peter Shaffer took this grisly anecdote as a starting point for what Simon Callow – the actor who first played Mozart on stage – describes as "a vast meditation on the relationship between genius and talent".
There is a vast literature exploring the relationship between low birthweight and adverse outcomes, using different methodologies to do so.
There is a vast literature exploring the relationship between fetal growth restriction and adverse outcomes, using different methodologies to do so.
As we leave ever more detailed online footprints — via purchasing, browsing and social relationships — a vast "big data" ecosystem has emerged to collect, process and resell this information.
I'm sure there must be a vast literature around family relationships, especially siblings.
In addition to containing a vast collective of causal relationships derived from healthy tissues, the Knowledgebase is particularly enriched in disease areas such as inflammation, metabolic diseases, cardiovascular injury, liver injury and cancer.
"We are the only M.A. in the study and history of contemporary design with an object-based approach," said Ms. Hackforth-Jones, highlighting the school's relationship with the auction house, which gives students the possibility of exposure to a hands-on relationship with a vast and changing selection of art objects passing through the sales rooms.
