Kent 171 and 55 for 1 (Denly 29*, Compton 17*) trail Warwickshire 549 for 7 dec (Yates 228, Maxwell 81) by 323 runs
A double-century from Rob Yates put Warwickshire in a commanding position after day two of their LV= Insurance County Championship game with Kent at Canterbury.
The visitors declared their first innings on 549 for seven, a lead of 378, before reducing Kent to 55 for one at stumps.
Yates hit his highest first-class score of 228 not out from 421 balls, with 23 fours and a six, having batted for nearly nine hours. Australia's Glenn Maxwell made 81 in his first championship appearance for four years and Henry Brookes was unbeaten on 52 as the visitors dominated throughout.
Chris Rushworth bowled Tawanda Muyeye early in Kent's second innings and although Ben Compton and Joe Denly survived till the close, the hosts are still 323 behind with two days remaining.
Warwickshire began the day on 155 for two and they'd nudged into a three-run lead when Sam Hain edged Arshdeep Singh and fell to a diving catch by Jordan Cox for 32.
Jacob Bethell immediately went on the attack, clubbing Hamid Qadri for a six that flew into the gardens on the Old Dover Road side of the ground. The ball was lost, somewhere in the vicinity of a dead pigeon it had apparently hit.
Kent's hopes were looking nearly as lifeless when Jack Leaning briefly revived them with two wickets in five balls. Bethell was out for 31, caught by a back-pedalling Arshdeep at deep mid-on for 31 and Ed Barnard went for a four-ball duck, narrowly surviving an lbw shout off the third ball he faced before getting caught behind.
This spasm of hope for the home side quickly subsided as Yates and Maxwell put on a stand of 124. The former reached three figures when he cut Arshdeep to third man and the lead was exactly 100 at lunch.
Maxwell looked set for a hundred, but he was caught behind chasing a wide delivery from Matt Quinn, though with the lead already past the 200 mark there was little celebration either in the middle or on the boundary.
The most dramatic moment of the afternoon session came when Yates hit Qadri for a six that went so far over the bowler's head that it ended up smashing a glass panel on the balcony of the Kent dressing-room.
Yates cruised past his previous highest score of 141 with a straight-driven four off Grant Stewart and it was 442 for six at tea.
Michael Burgess was subsequently out for 42, caught off Quinn by Harry Finch at backward point but Yates survived a major scare when he was on 199, chipping a ball from Qadri just out of reach of three fielders, before he drove the next ball through the covers to pass 200.
The declaration came as soon as Brookes had creamed Leaning for six to reach his half-century, leaving Kent with 14 overs to survive under increasingly ashen skies.
Muyeye lasted just five balls before Rushworth sent his off stump flying and although Denly and Compton made it to the close on 29 and 17 respectively, Kent will need something approaching a miracle over the next two days to avoid a damaging defeat.