Methods and apparatus for supporting use of multiple bandwidth parts, some of which are in a dormant state from the perspective of a User Equipment device (UE) are described. In various embodiments a multi-cell grant is supported in which a UE can be, and sometimes is, granted resources corresponding of an active bandwidth part (BWP) corresponding to a cell which is active from the UE's perspective and a BWP of a dormant cell with the multi-cell grant being transmitted to the UE on the active BWP of the active cell. Various features relate to timing determination operations used to determine downlink and/or uplink timing to be used for bandwidth portions corresponding to a dormant cell. In some embodiments a UE PRACH signal transmission on a bandwidth part of a dormant cell can be triggered by a control signal sent on a bandwidth part of an active cell.