Across:
   1. Trajectory of a papist (3)
   3,17dn. Heal fan quite deranged for star (5 7)
   6. Literary returns not done well (4)
   9. Being a star might involve opposite of hair care (6 5)
  10,25ac. No mackerel cooked without a star (3 6)
  11. Great sociably 30 cheeky fellow (6)
  12. No source of oil in terrible corn Delhi issues (8)
  14. They would hang around with slackers after mother left (9)
  15. Prompted 30 to leave 10 perhaps (4)
  19. Near the top of cap? Extremely! (4)
  20. In hindsight, a poet's only an alternative therapist (9)
  23. Understood to be illegal having representative in place of student (8)
  25. see 10 across
  27. see 2 down
  28. Equivalent of 1 in 20 hung about after Ms Peron a star (5 6)
  29,13dn. Judge reworking of 2 27: minus one star! (4 10)
  30. 7s and 11s definitely aren't, but some of them could be (5)
  31. Maxim was revolutionary (3)
Down:
   1. Look up to notice morass (6)
   2,27ac. Moving her in can suit star (9 3)
   3. Clams up in North East, taking month to quash nonsense (8)
   4. Cut grass has no vitamin (4)
   5. As 28 in US or 2 27 in Australia, news 3 across captured other about right (10)
   6. Kill or turn around 3 across and her 12 perhaps (6)
   7. 15 or 3 across perhaps were lured back after being freed from grip of weed (5)
   8. Rang lass who you then offended: more dead ends! (7)
  13. see 29 across
  16. Has more gravity than goes with work around uni (9)
  17. see 3 across
  18. Second place is poor for unusual dishes (8)
  21. Forged anvils in wood (6)
  22. see 26 down
  24. 90 year old dog put down with love, using paralytic essentially (5)
  26,22. Immediate result of composing hard new one (4 3 3)