What type of airspace is an Atlantic Low Control Area? Could someone explain what the blue zipper line 'Atlantic Low Control Area' is in the images below?

What type of airspace is this? How far off the coast does it start? Would it still be G to 1200 and E to 18000 in this area? Is this related to a Warning area which begins 12 NM off the coast? Why are there two parallel lines? I'm not really sure what questions to ask about it but I want to understand it well enough to be able to explain it in a check ride.
The Atlantic Low Control Area is a Class E area in international airspace, where domestic ATC procedures may be used for separation procedures.

Here are the relevant excerpts from FAA Chapter 19. Other Airspace Areas
Section 1. General


  Offshore/Control Airspace Areas are locations designated in international airspace (between the U.S. 12-mile territorial limit and the CTA/FIR boundary, and within areas of domestic radio navigational signal or ATC radar coverage) wherein domestic ATC procedures may be used for separation purposes. 


and


  Class A Offshore/Control Airspace Areas are identified as “High" (e.g., Atlantic High; Control 1154H). Class E areas are identified as “Low" (e.g., Gulf of Mexico Low, Control 1141L)


The two parallel lines differentiate floors of class E airspace that is neither 700 feet nor 1200 feet AGL (Above Ground Level).