The program that does prefix delegation is
radvd (Router Advertisement Daemon). Other IPv6 hosts on the link should automatically configure a globally routeable address from the announced prefix.
IPv6 does not require NAT as hosts which require Internet access are expected to have globally routeable addresses. You need to be careful in your Firewall rules to prevent infiltration from the Internet.
ISPs are expected to give out a /48 or /56 network block to their customers. This requires a bit of smarts on the ISP side to ensure each router gets a unique block. One /64 block will likely be used as the uplink to the IPS's network. The router is then free to announce as many /64s as from the rest of the block as it wishes. Likely only one would be used in this scenario.
There is an IPv6 DHCP implementation as well.
One quick setup which has been done is to configure the router to use 6to4 tunneling. radvd will autoconfigure for this setup, but it requires a publicly routeable IPv4 address.
radvd can't subdelegate prefixes it can automatically announce a /64 prefix based on an available routeable addresses. It also has Base6to4 to automatically announce the 6to4 prefix of the router. Subdelegation requires some planning and is beyond what should be expected of a plug and play configuration.
EDIT2: Like IPv4 IPv6 does not have a method to determine which network belongs on the networks connected to eth1 or eth2 base on the address assigned to the eth0 interface. Once you have multiple network segments you need to begin managing the addresses assigned to each segment. The good news is this can usually be done once.
IPv6 makes it easier as 5 and 8 can easily be given /49 or /50 subnets of the /48 delegated to 3. An alternate approach would be to configure 3, 5, and 8 as bridges on the same /64 subnet. In such a configuration, they would work as switches. Automatic subnet generation risk routers 5 and 8 both choosing to delegate the same subnet.
Plug and pray routers for home use just use a default private address block. They quickly break down when configured as shown in your diagram. Mixing routers with different default address blocks may work. Otherwise you need to ensure each router has different block of addresses.