“...There's now some scientists claiming that the various hominids all over
the world got gradually hominised gradually via evolution/gene-transfer
between populations etc., with Neanderthals eventually evolving more modern
traits etc., rather than a mass influx of modern humans from Africa in very
recent times....”

It seems to me that the above quote is on the right track. The
Multiregional idea seems to mean that a pre--human species or subspecies
came out of Africa and only later evolved to become the different sub-races
of man in different environments. This seems valid.

Ken