  We revisit staircases for words and prove several exact as well as asymptotic
results for longest left-most staircase subsequences and subwords and staircase
separation number, the latter being defined as the number of consecutive
maximal staircase subwords packed in a word. We study asymptotic properties of
the sequence $h_{r,k}(n),$ the number of $n$-array words with $r$ separations
over alphabet $[k]$ and show that for any $r\geq 0,$ the growth sequence
$\big(h_{r,k}(n)\big)^{1/n}$ converges to a characterized limit, independent of
$r.$ In addition, we study the asymptotic behavior of the random variable
$\mathcal{S}_k(n),$ the number of staircase separations in a random word in
$[k]^n$ and obtain several limit theorems for the distribution of
$\mathcal{S}_k(n),$ including a law of large numbers, a central limit theorem,
and the exact growth rate of the entropy of $\mathcal{S}_k(n).$ Finally, we
obtain similar results, including growth limits, for longest $L$-staircase
subwords and subsequences.
