I'll just add what I did with my own dataset of ribo depleted RNA-seq:
I took predicted enhancer-promoter interaction datasets from UCSC and counted RNA reads over the enhancer regions. I also had standard counts over actual genes. Then using the predicted gene partner for each enhancer, I correlated the Enhancer and Gene data (e.g. x-axis was counts over enhancer region, and y-axis was counts over the predicted gene partner for each enhancer region).
I saw moderate (~0.5) correlation. Meaning if an enhancer region had increased RNA, it's supposed target had a good chance of also having increased expression.
Generally speaking, most promoters only initiate transcription for a single gene, with a single gene potentially having multiple promoters driving multiple isoforms. Do you perhaps mean enhancers? Enhancers can drive or repress the expression of multiple genes.
yes! clearly the terminology on my side needs to improved!