Base stations and user equipments (UEs) for random access and contention resolution. A method for operating a UE includes receiving configurations for a first control resource set (CORESET) that includes a first number of resource blocks (RBs) in a frequency domain and a first number of symbols in a time domain, a second CORESET that includes a second number of RBs in the frequency domain and a second number of symbols in the time domain, and a reference signal received power (RSRP) threshold. The method further includes determining a first RSRP value and receiving a first physical downlink control channel (PDCCH). The first PDCCH reception is in the first CORESET when the first RSRP value is larger than the RSRP threshold and the first PDCCH reception is in the second CORESET when the first RSRP value is smaller than the RSRP threshold.