  Magnetic measurements on heavily overdoped $La_{2-x}Sr_xCuO_4$,
$Tl_2Ba_2CuO_6$, $Bi_2Sr_2CuO_6$ and $Bi_2Sr_2CaCu_2O_8$ single crystals reveal
a new type magnetization hysteresis loops characterized by the vanishing of
usual central peak near zero field. Since this effect has been observed in
various systems with very different structural details, it reflects probably a
generic behavior for all high temperature superconductors. This easy
penetration of magnetic flux can be understood in the picture of percolative
superconductivity due to the inhomogeneous electronic state in heavily
overdoped regime.
