Given a metric tree T we describe a construction that takes
several copies of T, identifies some points and edges, and
specifies a metric to obtain a connected metric graph G.
The natural map projecting G down to T is a tropical morphism,
i.e. a discrete analogue of morphisms from algebraic curves
to the projective line. The main question of this talk is
what metric graphs can be obtained out of such construction, 
i.e. for which G there are tropical morphisms from G to metric 
trees. We show via a deformation argument that all metric 
graphs are possible. When g := |E(G)| - |V(G)| + 1 is even 
we do a count of the number of ways G is realizable with 
such constructions and we get the g/2-th Catalan number.