If both parents have died, intestate, then yes, very simply put - their estates are shared equally between their children.
The Government only gets inheritance tax if the value of each child's share is above the current threshold (€542,544 for 2009)
The mere fact that there is no will does not mean the government get any share. The State (Government) is the ultimate beneficiary in an estate only where absolutely no next of kin at all can be traced.
As they died intestate there is no will - so I think you mean do you need a solicitor to take out the grant of Letters of Administration - no - this can be done by one of the children if they feel up to the task. The staff in the Probate Office are very helpful to personal applicants.