  We consider multi-type Galton Watson trees, and find the distribution of
these trees when conditioning on very general types of recursive events. It
turns out that the conditioned tree is again a multi-type Galton Watson tree,
possibly with more types and with offspring distributions, depending on the
type of the father node and on the height of the father node. These
distributions are given explicitly. We give some interesting examples for the
kind of conditioning we can handle, showing that our methods have a wide range
of applications.
