In this paper, we consider the predefined-time extended state observer (PTESO) design for a class of high-order strict-feedback systems subject to Hölder continuous nonlinearities and multiple disturbances. By developing an adaptive mechanism and using time-varying functions, a class of adaptive PTESOs is designed, in which the convergence time can be tightly and explicitly preset by only one parameter, irrelevant to the initial conditions. The adaptive mechanism is used to improve the transient performance under wide-range lumped disturbance. Moreover, thanks to the design of the time-varying gains, the PTESO could realize fast observation with trivial peaking observation errors. Finally, simulation results are provided to illustrate the effectiveness of the proposed observer.