Proportion of 2-generated $p$-groups of a given order

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For a prime $p$ and positive integer $n$, let $N(p^n)$ be the number of isomorphism classes of groups of order $p^n$, and let $T(p^n)$ be the number of isomorphism classes of groups of order $p^n$ which are 2-generated.

What can we say about the ratio $T(p^n)/N(p^n)$? Does it always have a limiting value of 1 as $n\rightarrow\infty$, in particular?