  Lie conformal algebras appear in the theory of vertex algebras. Their
relation is similar to that of Lie algebras and their universal enveloping
algebras. Associative conformal algebras play a role in conformal
representation theory. We introduce the notions of conformal identity and
unital associative conformal algebras and classify finitely generated simple
unital associative conformal algebras of linear growth. These are precisely the
complete algebras of conformal endomorphisms of finite modules.
