So where were Ann and Susannah in 1891, had Ann married ie?
Ann emigrated to the US not long after Susannah was born and either divorced her first husband and married my great-great-uncle or just conveniently forgot about her first marriage! But, oddly enough, in 1891 she was back in the UK visiting her mother in Eston when the census was taken. By then, though, she and Susannah had taken my great-great-uncle's surname, Branton (I suspect he was Susannah's biological father).
What I really wanted to know was whether Susannah was registered as Branton or Fawcett and a clue as to who her father was. I'm hoping the certificate will confirm that the Guisborough Susannah is "my" Susannah and at least one of these questions will be answered.
Thanks again for your help. You've helped me eliminate one of the false positives.
Just in case this helps anyone looking is this the census and passenger lists
1891 RG12; Piece: 4015; Folio: 10; Page: 13 - Middlesborough
Ann Branton 30 Cornwall
Susannah 4 Pensylvania US
Beatrice 6 months ‘’
Visitors Betsy Rogers 53
this looks to be Ann with husband Thomas
1881 RG11; Piece: 4858; Folio: 6; Page: 5
Thomas FAWCETT 24 South Eston Yorkshire Lab at Iron Stone Mines
Ann 20 St Dennis Cornwall
Incoming passenger listAnna Branton 30,
Susan 4 child & Beatrice 1 inft.
Birth Date: abt 1861
Age: 30
Port of Departure: New York, New York, United States
Arrival Date: Jan 1891
Port of Arrival: Liverpool, England
Ship Name: Celtic
Did they make a mistake with Susannah's name when leaving UK definately looks to read Lizzie

Anna Branton 30 dittoed as married,
Lizzie 5 child, Beatrice 1 Inft.
Arrival Date: 19 Aug 1891
Port of Departure: Liverpool, England and Queenstown, Ireland
Destination: New York
Ship Name: Teutonic
Was Ann's maiden name STONE?
marriage 1880 Middlesbro'
Thomas Fawcett name on same page Ann STONE
1871 RG10; Piece: 2221; Folio: 39; Page: 1
Betsey Stone Wid 34 (1881c married to Henry Rodgers)
Ann 9
St Dennis Cornwall (father is William 1861c)
Isabella 4 (1881 census Isabella Stone Rodgers age 14)
Mary Grigg W 76 mother