Maxima of random particles scores in Markov branching process with continuous time

We consider supercritical Markov branching processes with continuous time where every particle has one or two random scores. We are interested in maxima of these scores over the population. The class of nondegenerate limit laws for linear normed maxima is described. Limit copulas, upper and lower tail dependence coefficients are obtained for cases of two scores and two time points. Results are illustrated by the computer simulation. The work was partially supported by RFBR grants No. 07-01-00077, No. 07-01-00373.