Methods, apparatuses, systems, etc. for handling mobility in connection with protocol data unit (PDU) sessions are provided. Among these is a wireless transmit/receive unit (WTRU) that may receive, from a source access network (S-AN), a handover command in connection with a handover involving a multi-access protocol PDU (MA-PDU) session having one of first and second access legs associated with the S-AN. The WTRU may determine that the second access leg should be associated to the S-AN for the handover. The WTRU may send a session modification message to request modification of the MA-PDU session to cause the second access leg to become associated with S-AN The WTRU may establish a radio resource control connection with a target AN (T-AN), and the first and second access legs (e.g., as a combined access leg) may be associated with the T-AN.