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We consider the asymptotics of various estimators based on a large sample ofbranching trees from a critical multi-type Galton-Watson process, as the samplesize increases to infinity. The asymptotics of additive functions of trees,such as sizes of trees and frequencies of types within trees, a higher-orderasymptotic of the ``relative frequency'' estimator of the left eigenvector ofthe mean matrix, a higher-order joint asymptotic of the maximum likelihoodestimators of the offspring probabilities and the consistency of an estimatorof the right eigenvector of the mean matrix, are established.

Limit laws of estimators for critical multi-type Galton–Watson processes