Which router function advertises external routes in OSPF?

The router function that advertises external routes in OSPF is ASBR, which stands for Autonomous System Boundary Router. An ASBR is a router that connects an OSPF domain to another routing domain, such as another OSPF domain or a different routing protocol domain. An ASBR can redistribute routes from other routing domains into OSPF as external routes, which are carried in type 5 or type 7 LSAs. External routes have two types: E1 and E2. E1 routes include the cost from the ASBR to the destination, while E2 routes only include the cost advertised by the ASBR34.

References: OSPF External Routes ⋆ IpCisco, OSPF External Route selection algorithm - Cisco Community