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How do I write, southern Africa or Southern Africa?
Also, west Africa or West Africa? Any guiding remarks?
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Hi Chatvic, welcome to the forums!

Southern Africa
West Africa

It forms part of the whole country name, so it is capitalised.
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You have no choice with South Africa but both southern Africa and Southern Africa are common. I suppose many people capitalise southern for the simple reason that it looks better that way. In English, some people can capitalise even mother if they are talking about their own mother and want to be polite or respectful. To a large extent, this is more a matter of style and personal preference than grammar.

CB
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it is actually in lower case as southern Africa is not the actual name of the country unlike South Africa which is the full name of the country and is therefore in upper case.
 Cool Breeze's reply was promoted to an answer.
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Southern Africa is not a country. It's describing a a region of Africa. I.e. the southern region of Africa. Strictly speaking the "southern' is an adjective here, not part of a proper noun and therefore is not automatically capitalized unless the publication you are writing for has decided to capitalise it. South Africa by contrast is always capitalised as both words are part of the noun.