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To perform an outer join in a many-to-many relation using TypeORM, you can use the leftJoinAndSelect function to join two tables and select all entities from one table and matching entities from another. Here's an example:

@Entity()
class Book {
  @PrimaryGeneratedColumn()
  id: number;

  @Column()
  title: string;

  @ManyToMany(() => Author, author => author.books)
  authors: Author[];
}

@Entity()
class Author {
  @PrimaryGeneratedColumn()
  id: number;

  @Column()
  name: string;

  @ManyToMany(() => Book, book => book.authors)
  books: Book[];
}

const books = await getRepository(Book)
  .createQueryBuilder('book')
  .leftJoinAndSelect('book.authors', 'author')
  .orderBy('book.id')
  .getMany();

console.log(books);

In this example, we're joining the Book and Author tables using the @ManyToMany decorator, creating an outer join that selects all books and their matching authors. We're then using the leftJoinAndSelect function on the Book repository to perform this join, and ordering the results by the book ID. The output will be an array of books, each with an array of authors.