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Slavic countries tend to have Grandfather Frost.
The map does not mention the Dutch Sinterklaas (Saint Nicholas) from which the Dutch in New Holland gave the future United States Santa Claus.
Saint Basil beats out Saint Nicholas in Greece(!).
Some form of Father Christmas wins out in Western Europe.
Spain, Poland, Czech Republic, Slovakia, southern Germanic realm (Bavaria, Switzerland, Austria, norther Italy), and Hungary have explicitly historical people give out gifts.
Jesus is the gift giver only in the southern Germanic realm and Hungary.
The original Christmas gift givers (the magi) are "still" giving gifts only in Spain (where they give on Three Kings Day and not Christmas).