Can images and tables be always placed immediately after the paragraph they are first mentioned, even if white-space needed to move to another page?

I would like to ensure that when I mention a table/figure in the text, the figure/table will appear after that paragraph ends. Even if this means leaving the rest of the page blank and putting the figure/table onto the next page.

Is this possible?

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Yes, it is possible. You can achieve this goal by loading the float package and always using the [H] location specifier after \begin{figure} or \begin{table}. Note that the H specifier should not be combined with any other location specifiers. Thus, [Hhtbp] is not a legal location specifier.
@JimBo: You haven't provided any LaTeX code showing what you're actually doing; I'm therefore not sure I understand your question. I was assuming that you have placed constructs such as \begin{figure} ... \end{figure} between rather than inside paragraphs. If that's the case, the [H] specifier will force the float to be placed at that location on the page or (if there's not enough space left on that page) at the top of the following page. Either way, no new paragraph is allowed to start until the float is placed. Do you want to pursue a different approach? – Mico Aug 8 '12 at 11:31