  We consider a Feller diffusion (Zs, s $\ge$ 0) (with diffusion coefficient
$\sqrt$ 2$\beta$ and drift $\theta$ $\in$ R) that we condition on {Zt = at},
where at is a deterministic function, and we study the limit in distribution of
the conditioned process and of its genealogical tree as t $\rightarrow$
+$\infty$. When at does not increase too rapidly, we recover the standard
size-biased process (and the associated genealogical tree given by the Kesten's
tree). When at behaves as $\alpha$$\beta$ 2 t 2 when $\theta$ = 0 or as
$\alpha$ e 2$\beta$|$\theta$|t when $\theta$ = 0, we obtain a new process whose
distribution is described by a Girsanov transformation and equivalently by a
SDE with a Poissonian immigration. Its associated genealogical tree is
described by an infinite discrete skeleton (which does not satisfy the
branching property) decorated with Brownian continuum random trees given by a
Poisson point measure. As a by-product of this study, we introduce several sets
of trees endowed with a Gromovtype distance which are of independent interest
and which allow here to define in a formal and measurable way the decoration of
a backbone with a family of continuum random trees.
