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We classify the forward dynamics of all (plane) tree-valued Markov chains$(T_n,n \geq 1)$ with uniform backward dynamics. Every such Markov chain isclassified by a decorated planar real tree. We also show that under aninhomogeneous rescaling after trimming leaves $(T_n, n\geq 1)$ converges to arandom real tree in the Gromov--Prokhorov metric. This generalises and shedssome new light on work by Evans, Gr\"ubel and Wakolbinger (2017) on the binaryspecial case.

Continuum asymptotics for tree growth models