In extreme value analysis, it has recently been shown that one can use a de-randomization trick, replacing a random threshold in the estimator of interest with its deterministic counterpart, in order to estimate several extreme risks simultaneously, but only in an i.i.d. context. In this talk, I will show how this method can be used to handle the estimation of several tail quantities (tail index, expected shortfall...) in general dependence/heteroskedasticity/heterogeneity settings, under a weighted $L^1$ assumption on the discrepancy between the average distribution of the data and the prevailing distribution. This technique can also be used to deal with multivariate heterogeneous data, which cannot be handled with current methods.