Change height of a box, recalculate rubber lengths

Question

I'm using \setbox and \usebox to define a box, measure its default dimensions and render it later. During rendering, sometimes there is more vertical space available than measured initially, and I'd like to distribute this space between paragraphs. Is this possible using only the \mybox box in the example below?

\documentclass{scrartcl}
\pagestyle{empty}

\newbox\mybox

\begin{document}
  \setbox\mybox=\hbox{
    \begin{minipage}[t]{10em}
      \setlength{\parskip}{0ex plus5ex}
      First paragraph

      Second paragraph

      Third paragraph
    \end{minipage}
  }%
  %
  \usebox{\mybox}
  % How can I render the box with a specified height and distribute the paragraphs
  % according to the parskip?
\end{document}

Updating glue after changing width of a box seems related, but I don't see how to apply the technique shown there to change the height of a box.

Answer 1

After the removal of white spaces by line ends at the begin and end of the \hbox, the box \mybox is an \hbox, which contains a \vtop. Then the outer \hbox can be unpacked with \unhcopy or \unhbox (the latter clears the contents of the box). \lastbox catches the unpacked \vtop, which can be unpacked with \unvcopy and put into a new \vtop with the specified height:

\documentclass{scrartcl}
\pagestyle{empty}

\newbox\mybox 
\newbox\tmpbox

\begin{document}
  \setbox\mybox=\hbox{%
    \begin{minipage}[t]{10em}
      \setlength{\parskip}{0ex plus5ex}
      First paragraph

      Second paragraph

      Third paragraph
    \end{minipage}%
  }%
  %
  \unhcopy\mybox
  \setbox\tmpbox=\lastbox
  \vtop to 100pt{\unvcopy\tmpbox}
\end{document}