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Liverpool will play Sparta Prague in the last 16 of the Europa League, while Brighton have been drawn against Roma.
In the Europa Conference League, Aston Villa – the last remaining British team in that competition – must overcome former European champions Ajax.
The first legs of the ties will take place on 7 March, with the second legs to be played a week later on 14 March.
The Europa League knockout round play-offs, in which the runners-up from the Europa League group stages faced teams who finished third in the Champions League group stages, concluded on Thursday.
The eight group winners, seeded in Friday’s draw, advanced straight to the last 16 and will each play at home in the second legs.
That is also the case in the Europa Conference League where – like Liverpool, Brighton, West Ham and Rangers – Aston Villa will have the advantage of playing at home in the second leg next month.
Europa League last-16 draw
Sparta Prague v Liverpool
Sporting Lisbon v Atalanta
Qarabag v Bayer Leverkusen
Premier League leaders Liverpool sealed their place in the last 16 with a game to spare in November, avoiding February’s play-off round by topping their group.
The Reds, who have won the competition three times and finished runners-up in 2016, are still contesting four trophies this season and face Chelsea in the League Cup final on Sunday.
Liverpool won their only previous meeting with Sparta Prague in the last 32 of the 2010-11 Europa League, progressing 1-0 on aggregate after Dirk Kuyt scored late in the second leg.
West Ham, who also qualified in the penultimate round of group fixtures, were crowned Europa Conference League winners last season after reaching the Europa League semi-finals in 2022.
They have already beaten German club Freiburg twice in this season’s competition, winning 2-0 at home and 2-1 away against their Group A opponents.
Brighton, playing European football for the first time in the club’s history, beat Marseille in their final group game to progress as group winners.
Roberto de Zerbi’s side will take on last season’s runners-up Roma, who are sixth in Serie A and overcame Feyenoord in a penalty shootout on Thursday.
Aston Villa, back in Europe for the first time since the 2010-11 season, progressed in the Europa Conference League as group winners with 13 points from six games.
Europa Conference League last-16 draw
Servette v Viktoria Plzen
Maccabi Haifa v Fiorentina
Olympiacos v Maccabi Tel-Aviv