The Relayer run by the LayerZero team and reference implementation.
All User Applications will use the LayerZero Relayer by default.
The team runs and maintains a Relayer as a production asset for the ecosystem. It will soon be fully open-sourced so that anyone can fork and operate their own Relayer.
LayerZero Relayer assumes only a base gas for destination contract call, e.g. 200k gas for a call on Ethereum. It will only be enough for very simple applications.