Counterpart lease agreements

I have a query about leasehold and freehold.

Freehold houses in a housing estate with a management company do they still have lease agreements or what is the name of the document which informs the owner of the house of her obligations to paying managment fees keeping common area tidy etc.

Depends- duplex could be a lease for eg. But a house will usually have both a freehold conveyance of the title to the land plus a lease of easements. It is the lease or lease of easements that contain the covenants such as payment of management fees.