These are the Kearne entries, plus a few Kerns found along the way:
HO107/1593/30r Walton on Thames
Benjamin Kearn 32 b Wonersh
Ann 30 b Pyrford
Fanny 10 b Worplesdon
William 8 b Worplesdon
HO107/1593/ 43v Walton on Thames
Catherine Kearne 22 b Dublin
HO107/1597/344v Shalford
Henry Kearn 51 b Peper Harow
Dinah 40 b Worplesdon
Henry 22 b Wonersh
Isaac 20 b Wonersh
George 10 b Bramley
Joseph 8 b Bramley
HO107/1597/345r Shalford
William Kearn 23 b Wonersh
Ann 28 b Rudgewick Sussex
William 2 b Shalford
Ellen 1 b Shalford
HO107/1597/ 372r Shalford
Harriet Kern 18 b Bramley
HO107/1594/683v Godalming
John Kearn 44 b Godalming
Eliza 36 b Hull Yorkshire
HO107/1594/739r Godalming
Samuel Kearn 20 b Godalming
HO107/1594/300r & 300v West Clandon
? same family
Elizabeth Kearn 75 b Crawley Sussex
Robert Kearne 79 b Witley
HO107/1597/149r Haslemere
George Kearn 23 b Frensham
Maria 22 b Thursley
Ellen 1 b Haslemere
HO107/1594/157r Haslemere
William Kearn 26 b Haslemere
HO107/1594/508v Guildford St Mary
Emma Kearn 23 b Wonersh
HO107/1594/515r Guildford St Mary
Mary 16 b Bramley
HO107/1594/409r
Emma Kearn 20 b Worplesdon
HO107/1597/412r Wonersh
Robert Kern 39 b Godalming
HO107/1597/421r Wonersh
Sarah 49 b Send
William 14 b Wonersh
It's not possible to tell if some of these were with relatives

Nell