Tropical's Profile

I love tropical plants my garden has a very medditeranean feel to it, I have managed to get a good look to it all year round with splashes of colour in summer and a evergreen lush look in the winter. I have cordylines that have three quite large offshoots which we have just seperated from the parent plant, what i would like to know is what to do with offshoots to keep them and grow them on as a seperate plant is this possible.

Would really appreciate any feedback on this.