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We prove that the degrees of the first $\\nu_m^n:=n^{\\frac{m}{m+2}-\\epsilon}$ vertices are jointly, and uniformly, asymptotic to $\\{2(mn)^{1/2}\\bigl(W^{1/2}_{mj}-W^{1/2}_{m(j-1)}\\bigr)\\}_{j\\in [t]}$, and that with high probability (whp) the smallest of these degrees is $n^{\\frac{\\epsilon(m+2)}{2m}}$, at least. 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