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I am editing a longtable. Some of my cells contain a lot of text. Page breaks seem to happen only where table rows end/begin. I'd like, however, for the rows to span pages; it's fine with me if, for example, the first few lines of a row are at the end of one page and the rest of the row's lines are on the next page.

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it's not in general possible, consider if one cell is a large image and the next cell is text how would it break? p columns are essentially parboxes that do not break. –  David Carlisle Oct 21 '12 at 19:44
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Well, try to think about it for a while. Where should the cells be broken if the lines in them are not equally high? In one cell you nicely reach the "full height of a page" which in the other one you get an empty space at the bottom. Nah, this cannot work. –  tohecz Oct 21 '12 at 20:51
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@DavidCarlisle Sounds like an answer to me! –  Joseph Wright Nov 21 '12 at 8:32
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2 Answers

It is not in general possible. Consider if one cell is a large image and the next cell is text how would it break? p columns are essentially \parboxes that do not break.

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pagebreaks inside a cell are in general not possible but you can work with a trick if you really need a break. However, it makes no sense if you have a lot of such tables or pagebreaks.

Set the long table as usual and have a look into the pdf output of the cell where a pagebreak maybe usefull. Now insert in that cell at the last word of that line

 first col & ... some text \parfillskip=0pt \tabularnewline
           & and the follwing text which is on the next page.

With setting \parfillskip=0pt you'll get a left and right justified line.

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