A tree that was uprooted, but there remained in it a root, it is exempt. And how much must the root be? Rabban Gamliel says in the name of R' Elazar ben Yehudah the man of Bartosa: Like the stretching needle.

[If] a tree was uprooted but had a layer, and it survives from it, then the old [tree] becomes like the layer. [If] he layered it year after year, and it was severed, he counts from the time that it was severed.  An extension of grapevines, and an extension upon an extension, even though he layered them in the ground, it is permitted. R' Meir says: Where its strength is sufficient, [it] is permitted; but where its strength is insufficient, [it] is forbidden. And so too, a fruit-laden layer that was severed, if it increased by [one part] in two hundred, it is forbidden.