This is a Sirius question! :) Actually, that's the answer -- Sirius.
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If you are not counting the Sun, then it would be Sirius, only about 8 light years distant, which is clearly visible in both hemispheres. It is the brightest star in the sky other than the Sun.
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Sirius is at a declination of -16 degrees, so the brightest star in the entire sky is also the brightest for the southern sky
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Would that be in absolute or apparent magnitude?