DHCP and subnets

[whatshakin]

Hello folks, Please clarify this for me.    Hypothetical example: Campus LAN with multiple buildings.  Each building on its own vlan and with its own subnet addressing scheme. All buildings tied in to a Catalyst 5500 which has RSP doing all the inter-vlan routing.  Data center using a single DHCP server with multiple scopes (one scope per vlan/subnet etc) to supply all vlans/subnets with their respective ip addresses.  I want to understand how the DHCP server knows how to hand out the correct ip address from the corresponding subnet to the workstations that request them.  I have come to believe that initially DHCP servers have no idea whom is requesting an address, they just hand them out to whoever asks...this is what is confusing.  I understand that each Vlan needs its own gateway address where the workstations aim their broadcasts and there an ip helper-address statement in the RSP for each vlan, but I still don't understand how the DHCP server knows how to hand out the appropriate address when it has multiple scopes enabled.   TIA for any clarification you can offer.