The network scale-up method is a social network estimator for the size of hidden or hard-to-count subpopulations. These estimators are based on a simple model which have however strong assumptions. The basic idea is that the proportion of the mean number of people known by respondent in a subpopulation E of T of size e is the same of the proportion that the subpopulation E forms in general population T of size t: m/c=e/t, where c is the number of persons known by each respondent and m is the mean number of persons known by each respondent in the subpopulation E. The persons known by every subject is called the "social network", and its size is c, estimated by several estimators proposed in the recent literature. In this paper we present a Monte Carlo simulation study aimed at understanding the behavior of the scale-up method type estimators under several conditions. The first goal was to understand what would be the ideal number of subpopulations of known size to be used in planning the research. The second goal was to analyze what happens when we use overlapped subpopulations. Our results showed that with the scale-up estimator we always obtain biased estimates for any number of subpopulations employed in estimates. With the Killworth's ML estimator, the improvement of scale-up method, we have substantially unbiased estimates under any condition. Also in case of overlapping, and increasing the degree of it among subpopulations, bias raises with scale-up method, instead it remains close to zero with ML estimator.