There are many managed relational database services available in the market, but the top ten providers are generally considered to be:

1. Amazon RDS: A fully managed relational database service offered by Amazon Web Services. It supports multiple database engines such as MySQL, PostgreSQL, Oracle, MS SQL and more.
2. Azure SQL Database: A fully managed relational database service offered by Microsoft Azure. It is based on the SQL Server engine and supports both PaaS and IaaS deployment options.
3. Google Cloud SQL: A fully managed relational database service offered by Google Cloud Platform. It supports multiple database engines such as MySQL and PostgreSQL.
4. Oracle Cloud Infrastructure: A fully managed relational database service offered by Oracle Cloud Infrastructure. It supports multiple database engines such as MySQL, PostgreSQL, and Oracle Database.
5. IBM Cloud SQL Query: A serverless, fully managed relational database service offered by IBM Cloud. It supports multiple database engines such as MySQL, PostgreSQL, and IBM Db2.
6. Alibaba Cloud RDS: A fully managed relational database service offered by Alibaba Cloud. It supports multiple database engines such as MySQL, SQL Server, and PostgreSQL.
7. Aiven: A fully managed relational database service that offers a variety of database engines such as MySQL, PostgreSQL, and Redis.
8. ScaleGrid: A fully managed relational database service that provides a platform for hosting, managing and scaling MongoDB, Redis, MySQL, and PostgreSQL on public, private, and hybrid clouds.
9. MariaDB: A fully managed relational database service that is based on the open-source MariaDB database engine. It is fully compatible with MySQL and offers additional features such as column store and data lake integration.
10. Heroku Postgres: A fully managed relational database service offered by Heroku which is a PaaS provider. It’s based on the open-source PostgreSQL database engine and it’s integrated with Heroku’s platform, making it easy to deploy.