Multiple DHCP Servers - can each supply addressess to 'local' clients only?

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http://serverfault.com – I have read the canonical question Can I have multiple DHCP servers on one network?, and have a follow up question. A simplified explanation of my setup... client1 ----- router1 ----------------- router2 ----- client2 Essentially, I would like client1 to get an address from router1 (& client2 from router2). These clients download firmware from a TFTP server on the router they're connected directly to (TFTP address is same as default gateway address), so I don't want client1 getting firmware from router2 when it is connected directly to router1. The reason for this logic is that if rou ()