Managed hosting is when you own and run a site, but the hosting company does the behind-the-scenes tech stuff like installation and updates.
You can follow them at @tklk
There's also a well-established company called Masto.host offering #Mastodon managed hosting:
You can follow them at @mastohost
(Thank you to @Hau for the tip about Spacebear )
mastodon.at is a microblogging site that federates with most instances on the Fediverse.