We report on the London penetration depth ab (0), measurements, and second peak H determination in Bi 2 Sr 2 Ca 1Ϫx Y x Cu 2 O 8ϩ␦ ͑Bi-2212͒ crystals with different doping levels. By combining cationic substitutions and oxygen pressure annealings, crystals with a doping state going from the underdoped to overdoped regime have been obtained. The corresponding ab (0) values, deduced from reversible magnetization measurements have allowed us to evidence a ''boomerang'' shape for the T c ͓1/ ab 2 (0)͔ curve in the 0.8рT c /T c max р1 region. Moreover, other T c ͓1/ ab 2 (0)͔ values for superconducting crystals of Hg-and Tl-based cuprates are found to fit well with this boomerang path, demonstrating its universal nature. The overdoped side of the boomerang for the Bi-2212 crystals clearly shows that 1/ ab 2 (0) decreases as the doping level is increased. Since by the same time the characteristic field of the fishtail H monotonously increases, we have thus established that H increases with 1/ ab 2 (0) decreasing. Consequently, the linear relation H ϭ⌽ 0 / ab 2 (0) predicted by the electromagnetic model cannot account alone for the present experimental results in the overdoped regime.