First, I'd ask how's the health of the plants otherwise - any signs of poor growth or yellowing or leaf loss at the top, or obvious problems with the trunks, i.e., sogginess or peeling? A lot of cordylines suffered during last winter, and their response has often been to throw out new plantlets at the base or up the undamaged parts of the stem or trunk. If your plants are perfectly healthy at the tops, then you can try to remove some of the plantlets at the base - you need to get a good piece of root with each one though, so dig around a bit and see if its possible to find some with roots attached that you can cut off with a very sharp knife, then pot them up. As for the shoots further up, if you don't want them, you can remove them, or leave them to grow on into new branches, but I suspect they're there because the top's unhealthy, so check first.

Your reply is much appereciated. Thank You