I taught that the battle groups were to be made up of companies form each of the particapiting countries, for example, Ireland would provide a logistics comapny to support the bettle group they have joined (previously rumoured to be with Sweden & Finland, However they have already started to cross train).
So in a nutshell, if Ireland were to join any of the battlegroups, I would see the heavy equipment required such as transport aircraft and navel vessels provided by other member states.