$Background:$ Previous measurements of $beta$-delayed neutron emitters comprise around 230 nuclei, spanning from the $^{8}$He up to $^{150}$La. Apart from $^{210}$Tl, with a minuscule branching ratio of 0.007%, no other neutron emitter is measured yet beyond $A=150$. Therefore new data are needed, particularly in the heavy mass region around N=126, in order to guide theoretical models and to understand the formation of the third r-process peak at $Asim195$. $Purpose:$ To measure both, $beta$-decay half-lives and neutron branching ratios of several neutron-rich Au, Hg, Tl, Pb and Bi isotopes beyond $N=126$. $Method:$ Ions of interest are produced by fragmentation of a $^{238}$U beam, selected and identified via the GSI-FRS fragment separator. A stack of segmented silicon detectors (SIMBA) is used to measure ion-implants and $beta$-decays. An array of 30 $^3$He tubes embedded in a polyethylene matrix (BELEN) is used to detect neutrons with high efficiency and selectivity. A self-triggered digital system is employed to acquire data and to enable time-correlations. The latter are analyzed with an analytical model and results for the half-lives and neutron-branching ratios are derived using the binned Maximum-Likelihood method. $Results:$ Twenty new $beta$-decay half-lives are reported for $^{204-206}$Au, $^{208-211}$Hg,$^{211-216}$Tl,$^{215-218}$Pb and $^{218-220}$Bi, nine of them for the first time. Neutron emission probabilities are reported for $^{210,211}$Hg and $^{211-216}$Tl. $Conclusions:$ The new $beta$-decay half-lives are in good agreement with previous measurements in this region. The measured neutron emission probabilities are comparable or smaller than values predicted by global models like RHB+RQRPA.
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