Eukaryotes have multiple types of nuclear RNAP, each responsible for synthesis of a distinct subset of RNA.  All are structurally and mechanistically related to each other and to bacterial RNAP:
Eukaryotic chloroplasts contain an RNAP very highly similar to bacterial RNAP ("plastid-encoded polymerase, PEP"). They use sigma factors encoded in the nuclear genome.
Chloroplast also contain a second, structurally and mechanistically unrelated, single-subunit RNAP ("nucleus-encoded polymerase, NEP"). Eukaryotic mitochondria use POLRMT (human), a nucleus-encoded single-subunit RNAP. Such phage-like polymerases are referred to as RpoT in plants.