We present the results obtained from systematic studies of positron creation for a series of heavy-collision systems, with united charge Z,=Z I+Z 2 ranging from Z,= 164 (Pb+Pb) to Z,,= 184 (U+U) at bombarding energies close to the Coulomb barrier, using the Orangefl-spectrometer at GSI. For each collision system studied, the dominating continuous distributions due to quasiatomic and nuclear positron emission are determined accurately. This is essential in obtaining the characteristics of the still unexplained monoenergetic positron lines which appear in the energy range between 200 keV and 400 keV. Our results are compared with coupled-channels calculations for quasi-atomic positron creation. The latter describe quite well the global features of the measured spectra, but overestimate systematically their absolute values. From the comparison, a common normalization factor of about 0.75 can be established for the calculated spectra. In particular, the dependence on Z,, of the measured emission probabilities was found to follow a power law (ocZ,~95-+~), in fair agreement with the theoretical prediction.