The paper considers a supercritical, p-dimensional Markov branching process (MBP). Based on the finite and the infinite lines of descent of particles of this p-dimensional MBP, it constructs an associated 2p-dimensional process. The paper shows that such a process is a 2p-dimensional, supercritical MBP. This 2p-dimensional process retains the branching property when conditioned on the sets of extinction and non-extinction. Asymptotic results and central limit theorems for the associated process and the original process are established by using the results of Gadag and Rajarshi.
