As the saying goes, possession is nine-tenths of the law (Wikipedia).
Just about any web-based property is owned by the person (or company) who owns the email address that allows access to that property. Email addressees are owned by the person who controls the access to the email account at the email provider, i.e. the login and password. (For simplicity, I'm ignoring the fact that the individual's listed name on the email account can come into play in ownership disputes).
A Facebook page is owned by the owner of the administrative email for the account at that service. A domain is owned by the domain registrant, who opens an account at a domain registrar with an email and registers the domain. The domain registrant administers the ownership of the domain via an administrative email, and that email owned by the person who has the access to that email account.
Very basically, in your situation, if you want to "establish legal ownership" of a web property owned and/or administered by someone else, you determine if there is a contract in place (written or verbal) that established your partial ownership to the property, or an agreement to transfer full ownership of the property to you at some point. See Elements of a Contract — Judicial Education Center.
If there is an agreement or contract to transfer full ownership to you, execute the contract. Have everyone sign off on it and do the technical transfer of the property, i.e. change ownership and access of the email account associated with the property.
If there is an agreement or contract that you have partial ownership and you want full ownership, you attempt to renegotiate the contract, if both parties agree to renegotiate. Or you go to court and let a court decide the status of the contract.
If there isn't an contract and/or agreement in place regarding your current partial or future ownership of the property, you're out of luck. Whoever owns the property owns it.
You can go to court alleging something, like breach of contract, or you deserve the property (such as a domain or email address or Facebook page) because it's the same as your business name, but that's your choice.
Further, in particular to domain names, there is also a dispute resolution process Uniform Domain-Name Dispute-Resolution Policy - ICANN that seeks to resolve trademark-based domain-name disputes, which may or not be relevant in your question, which is primarily about ownership. Facebook also has a trademark-based domain-name dispute resolution process.