Deal the cards to the players

05AB1E, 3 1 byte

Saved 2 bytes thanks to Adnan

ι

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Explanation

ι  # uninterleave

Does exactly what the challenge asks for

R, 46 25 bytes

function(A,n)split(A,1:n)

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splits A into groups defined by 1:n, recycling 1:n until it matches length with A.

Perl 6, 33 24 bytes

->\b{*.classify:{$++%b}}

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Anonymous curried code block that takes a number and returns a Whatever lambda that takes a list and returns a list of lists. This takes the second option when given a number larger than the length of lists, e.g. f(4)([1,2,3]) returns [[1],[2],[3]]

Explanation:

->\b{                  }  # Anonymous code block that takes a number
     *                    # And returns a Whatever lambda
      .classify           # That groups by
               :{$++%b}   # The index modulo the number