The 53-year-old from Oakfields, Dorking, died after the Audi A3 he was travelling in left the road and collided with a tree on Sunday May 29 on Faygate Lane.
Mr Smith’s family have paid tribute to him as “kind, caring and lovable.”
His children Chloe, Jade, Rachel and Sophie, his step-son Lee, his sister Diane and the rest of his family said in a statement: “Our dad was the type of bloke that could walk into a dark room and light it up just with his presence.
“He was respected and loved so much by his family and friends and that’s down to his kind, caring, lovable nature.
“He was always there for everyone especially his family. He adored his grandchildren and we will all make sure that as they grow they will remember him just in the same way as we all will.
“Dad was an all-round genuine, kind loving and funny man. We all love you and will see you on the other side. Xxx”
A 37-year-old woman driver suffered serious injuries in the crash and remains in a serious condition in the Royal Sussex County Hospital, say police.
Anyone who witnessed the crash or who may have seen the Audi in the area around that time is asked to email [email protected] or call 101 quoting Operation Twickenham.