Permanent random number (PRN) and collocated random number (CRN) sampling are practical methods of controlling overlap between different samples. The techniques can be used for overlap control between samples for the same survey selected at different time periods or between different surveys at the same time period. Although the methods are in wide use, their properties, when a population is changing due to births and deaths, have not been studied extensively. Ideally, each technique should produce a sample proportionally allocated to births and persistent units when equal probability sampling is used. We present theoretical and empirical results showing the circumstances where proportional allocation is approximately obtained. We also discuss important cases where PRN and CRN sampling are substantially different in their coverage of birth and persistent units.