Why does signaling overhead for time synchronization scale up with the number of transmitter nodes in a multiple access system? I was recently reading about random multiple access methods without time synchronisation (of the pure Aloha type). In this paper it is stated that, 


  The need for transmitter synchronization is a major drawback for large networks as the signaling overhead scales up with the number of transmitters independently from their traffic activity factor.


I understand that oscillators tend to drift in time and present instabilities depending on the technology, operating conditions, etc., and therefore a reference signal must be given by the central node with a periodicity that depends on the desired accuracy and the transmitter's clock drift.

I would like to know why there is also a dependency on the network size.

EDIT: The only scenario I can think of where signalling scales up with the network size, is a distributed network (but in that context, we usually talk about logical clocks and not about hardware clocks/oscillators). Note also that the network described in the paper has a star topology, so a periodic broadcast message from the central node would do, independently on the number of users in the network.
Let's look at it a bit more in context:


  Moreover, E-SSA (as SSA) has another major advantage over SA/DSA/CRDSA
  i.e. its truly asynchronous RA nature eliminates the need to maintain
  accurate slot synchronization among all transmitters unlike the case
  in SA/DSA/CRDSA.  
  
  The need for transmitter synchronization is a major
  drawback for large networks as the signaling overhead scales up with
  the number of transmitters independently from their traffic activity
  factor. 
  
  The capacity of asynchronous collision channel without
  feedback was investigated by Massey in his seminal paper together with
  protocols sequences for achieving the capacity boundaries [17].


If I understand well, this is not about frequency locking, but about time slot synchronization: the synchronization occurs on a time scale that is orders of magnitude higher than the oscillator period.

In time division multiplexing, there is a guard period at the end of each time slot where nobody should transmit, both to prevent interference and to allow synchronization. 
Because this guard interval is present at each time slot, the sun of guard interval times can be considered to be an overhead that varies with the number of time slots (i.e. for the max. number of users the system is designed for).