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Ebbsfleet have been at home to King's Lynn Town in the FA Trophy.
The draw for the second round was made on Monday afternoon.
Kevin Watson's Fleet side reached this stage after a comfortable 2-0 win at Enfield Town on Saturday.
King's Lynn are top of National League North and knocked out Andy Hessenthaler's Dover in the previous round, 4-2 on penalties following a 2-2 draw in extra-time.
They have lost just twice this season and boast former Fleet striker Michael Gash among their squad.
Tonbridge, who came from 2-0 down to force a midweek replay at Hampton, have the chance to visit National League Yeovil Town if they win on Tuesday night.
Yeovil eased past Welling 3-1 in the first round at the weekend.
Winners will receive £5,250 in prize money while losing clubs will pocket £1,750.
The ties are due to take place on Saturday, January 11.
