  We show that large critical multi-type Galton-Watson trees, when conditioned
to be large, converge locally in distribution to an infinite tree which is
analoguous to Kesten's infinite monotype Galton-Watson tree. This is proven
when we condition on the number of vertices of one fixed types, and with an
extra technical assumption if we count at least two types. We then apply these
results to study local limits of random planar maps, showing that large
critical Boltzmann-distributed random maps converge in distribution to an
infinite map.
