Many environmental variables are continuously scattered over a region and the target parameter turns out to be the spatial total of the variable. In this setting, the design-based approach under the continuous-population paradigm may be conveniently considered. This design is carried out by locating sample sites according to stratified protocols based on a regular tessellation of the region. Such stratified designs are used in the field since they allow for an even sampling coverage of the study area. In this paper we show that the spatial total estimators under tessellation stratified designs are very accurate and normally distributed for large samples. Copyright © 2010 John Wiley & Sons, Ltd.