A novel mth best average biased received power (ABRP) user association (UA) scheme is proposed for K-tier heterogeneous networks, where a user is associated with the closest base station (BS) of the kth tier having the mth strongest ABRP, k + 1 , 2 , … , K . By using stochastic geometry and Poisson point processes, the authors perform the analysis of the UA probability that a typical user is associated with a BS that has the mth strongest ABRP as well as the downlink signal-to-interference-noise ratio (SINR) coverage performance. The obtained results show that, for a given tier k, when the layer's position in the ordered set of ABRPs is not equal to m and the power P k or density λ k of BSs is relatively small, i.e., P k 1 increases monotonically with P k or λ k . Contrarily, it decreases. For the other UA probabilities, the opposite results are achieved. Additionally, the results also show that the coverage probability of the downlink SINR of the tier k always increases with power P k , which is consistent with the one in the conventionally best ABRP scheme. However, for other tiers, the corresponding downlink SINR coverage probabilities do not behave monotonically with the power P k .