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All answers having "Celebrity" as clue:

3 Character Answers:

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CAR

VIP



4 Character Answers:

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FAME

IDOL

LION

NAME

STAR



5 Character Answers:

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ECLAT

GLORY

GROUT

RURAL



6 Character Answers:

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RENOWN



7 Character Answers:

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BIGNAME

STARDOM

WIGGING



8 Character Answers:

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EMINENCE

EXCHANGE



9 Character Answers:

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SUPERSTAR



10 Character Answers:

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FAMOUSFACE

MOOVIESTAR

PROMINENCE

REPUTATION



11 Character Answers:

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DOUBLEDUTCH

PERSONALITY

STETHOSCOPE



13 Character Answers:

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HOUSEHOLDNAME