We have performed a study of the magnetic hysteresis of (Hg1-xRex)Ba2Ca2Cu3
O8+delta samples with two "extreme" Re-substitutions in a temperature inter
val close to T-c. We observe a strong asymmetry of the magnetization loops
that can be associated with grains surface barriers or reversible magnetiza
tion. We also determined the temperature dependence of the first penetratio
n field and the irreversibility field of the grains, and the field dependen
ce of the magnetization curve width. The results suggest that the optimum p
inning level is located at 0.09<x<0.24.