You can configure a BGP device to advertise the default IPv4 route to a specific neighbor.
device# configure terminal
device(config)# router bgp
device(config-bgp-router)# local-as 1000
device(config-bgp-router)# address-family ipv4 unicast
device(config-bgp-ipv4u)# neighbor 10.4.4.4 default-originate
device# configure terminal device(config)# router bgp device(config-bgp-router)# local-as 1000 device(config-bgp-router)# address-family ipv4 unicast device(config-bgp-ipv4u)# neighbor 10.4.4.4 default-originate