  We study three families of labelled plane trees. In all these trees, the root
is labelled 0, and the labels of two adjacent nodes differ by $0, 1$ or -1. One
part of the paper is devoted to enumerative results. For each family, and for
all $j\in \ns$, we obtain closed form expressions for the following three
generating functions: the generating function of trees having no label larger
than $j$; the (bivariate) generating function of trees, counted by the number
of edges and the number of nodes labelled $j$; and finally the (bivariate)
generating function of trees, counted by the number of edges and the number of
nodes labelled at least $j$. Strangely enough, all these series turn out to be
algebraic, but we have no combinatorial intuition for this algebraicity. The
other part of the paper is devoted to deriving limit laws from these
enumerative results. In each of our families of trees, we endow the trees of
size $n$ with the uniform distribution, and study the following random
variables: $M\_n$, the largest label occurring in a (random) tree; $X\_n(j)$,
the number of nodes labelled $j$; and $X\_n^+(j)$, the number of nodes labelled
$j$ or more. We obtain limit laws for scaled versions of these random
variables. Finally, we translate the above limit results into statements
dealing with the integrated superBrownian excursion (ISE). In particular, we
describe the law of the supremum of its support (thus recovering some earlier
results obtained by Delmas), and the law of its distribution function at a
given point. We also conjecture the law of its density (at a given point).
