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It has been known for a few years that the occupation measure of severalmodels of embedded trees converges, after a suitable normalization, to therandom measure called ISE (Integrated SuperBrownian Excursion). Here, we provea local version of this result: ISE has a (random) H\"{o}lder continuousdensity, and the vertical profile of embedded trees converges to this density,at least for some such trees. As a consequence, we derive a formula for thedistribution of the density of ISE at a given point. This follows from earlierresults by Bousquet-M\'{e}lou on convergence of the vertical profile at a fixedpoint. We also provide a recurrence relation defining the moments of the(random) moments of ISE.

The density of the ISE and local limit laws for embedded trees