If Brits take over South America in 1800s-1860es... then they could intefere in the ACW and dissolve and takeover ( incorporate in Canada ) USA?
Thus, British super-Argentina ( like in my link ) would possess most if not all of S America, and British super-Canada will hold most if not all of N America.
The non-English speaking peripheral territories could be incorporated in these 2 Brit unions the same way French-speaking Louisiana or Quebec were integrated in OTL respectivelly USA and Canada.
The compactly populated by "latinos" ( spanish and portugese speakers ) territories could be held separatelly as "colonies" = non-self-governing entities until they are admitted in the British unions when the British very intensive immigration policy ( with usual mixture of Central AND Eastern Europeans - Brit Argentinized and Canadized respectivelly - tips the balance into English speaking majorities. ).
THUS:
British N America and British S America will:
- engulf the whole of the continents
- meet eachother at Nicaraguan canal built with joint effort by the two Unions with investment from the metropoly - UK.
- replace the existing Spanish and Portugese speaking majorities by new English speaking immigration and natural growth populations.
- British Empire will such way furnish itself with TWO super-USA level "white", settler Dominions.
- the "empty" lands would exist as long as non-self-governing territories within the structure of these Unions - until enough internal new-population pressure, economy and internal policies make it possible and necessary to be incorporated and established new member-States. In late 1990es-early 2000es most if not all of the total area of the both Americas shall turn into mosaic of member-states.
- British Super-Canada and Super-Argentina would be integrated within the British Empire sharing currency, customs, military ... etc. but later could be sought full integration with UK, turning it into United Kingdom of England, Ireland, Scotland, Wales... together with 100+ N and S British American "home nations" + several dozens of such African and Australia-Oceania and Asian ( Pearl river basin area, Hong Kong, Strait Settlements - Singapore+, Borneo... ) entities. Non-federal, non-imperial, but unitary United Kingdom with devolved local authorities in each "home state" and supremacy of the London Parliament.
- The only non-settler , hence non-full-member territories of the British Empire would be the Indian Empire, to which could be attached the non-settler territories in Africa, Arabia and SE Asia.
- such world would possess almost perfect Oceanic vs. Land geopolitical dichotomy.
UK+Indian Empire = British Empire vs. German-Russian domination of Eurasia.