His Dark Materials - North America Map

My best guess at a political map of this continent in Philip Pullman's His Dark Materials series (laid over the borders of our own world, for comparison).

Hat tip to this map for getting me started:


In-universe geography information was drawn from these references:
Wikipedia's HDM glossary
the His Dark Materials Wikia
the Bridge To The Stars wiki

The general theory is that the United States, at least in its "expanding ever westward and indiscriminately snapping up territory along the way" incarnation, never happened -- so a lot of the historical borders that it swallowed still stand.

From the top down...


Groenland and Fireland
The same as our-world Greenland and Iceland (with the latter being named for its volcanic activity instead of its glaciers).


Beringland
Independent country named for the European who first explored it, Vitus Bering. Corresponds to our-world Alaska, the Yukon, and the Northwest Territories.


New France
An expansion of the our-world New France before its dissolution in 1763. Comprises most of our-world Canada, plus the land included in the Louisiana Purchase (bounded by the Mississippi River to the east, and the Rocky Mountains to the northwest).


Mejico (Hispania Nova)
Corresponds mostly to the our-world Mexico (formerly New Spain) as of about 1845. They've lost the territory claimed by Texas, but never lose that involved in the Mexican Cession (bounded by the 42nd Parallel to the north, and the Rio Grande to the east).


Florida?
In our world, Florida was also another claim by New Spain until it was ceded to the United States (as part of a treaty in which we agreed to, get this, renounce all claim on Texas. Guess how long that lasted). Which means that, in this world, it could have stayed connected to New Spain until those colonies declared independence, at which point it would end up part of Mejico.

Alternatively, the Seminole Wars could have had a different outcome, leaving Florida an independent state under largely Native American control.


Republic of Texas
Corresponds to the short-lived our-world Republic of Texas. Borders are defined by (clockwise from top) the Arkansas River, the Red River of the South, and the Rio Grande.


New Denmark?
Most likely the name of a multinational region, if not the name of the entire continent. (Lee Scoresby is described as being from the Republic of Texas, but is also "from New Denmark.") If the books are misleading and it's a country after all, the salmon-colored region is where I would put it.


Unspecified territory
The unlabeled white region on the west coast is our-world Oregon Country/the Columbia District (bounded by the 42nd Parallel to the south, and 54°40′ to the north). I don't know which New World nation would most likely have snapped it up in this universe, or if it would have become one more independent nation in its own right. History buffs who have theories are welcome to weigh in here.

(One possibility: part or all of it became realized as the nation of Cascadia.)

Central America is referred to in-universe as The Isthmus. Specific national boundaries within it, as well as in the islands of the Caribbean, never come up.