As I know, In the contention-free mode, the eNB can uniquely identify the UE by a received preamble sequence, due to the fact
that the preamble to be used has been communicated to the UE in advance. Such a scenario is possible in certain cases,
e.g., during a handover between two eNBs.
In on demand SI request RACH, RACH-ConfigDedicated mode used & it is used for handover to the cell. So I think in this case contention-free RA procedure will use.
Waiting for other expert comment !!