The Dublin Regulation is, in fact, a European agreement. Currently, the Dublin III Regulation (EU Regulation No. 640/2013 of 26 June 2013) is applied, which has replaced the previous Dublin Agreement and the Dublin II Regulation. At present, a new version of the agreement (Dublin IV regulation) is being discussed. The Dublin Regulation determines which of the 32 Dublin countries is responsible for reviewing an asylum application. If you leave the Dublin State that is already responsible for your asylum case, the authorities would probably return you there. That is referred to as transfer (“Überstellung”). It is different from deportation (“Abschiebung”) which means sending a refugee back to their country of origin or to the country they have fled.
The Dublin Regulation does not mention whether and how newcomers in Europe should be “distributed”. The answer to these questions is specified in the Common European Asylum System (CEAS) was created. The Dublin Regulation is only a part of the Common European Asylum System.