Solution to 15A has been deliberately left unsolved and is to be answered by a non-regular/novice commenter, with proper annotation. Those who have answered earlier in the week, please give others a chance.
Open for anyone to answer, if not solved by 1 PM.
ACROSS
1 & 4 Time to levitate! Captivating line by poet about love and abandon! (5,9) THROW OVERBOARD {T}{H{ROW}OVER}{B{O}ARD}
4 See 1
11 Smell from well-to-do urban centres (5) ODOUR [T]
13 America baptised initially by taking over English ecclesiatic institution (5) ABBEY {A}{Ba...d}{B{E}Y}
15 Irritate less! No to an extent! (3) A?Y ()
16 Idiot questions king's ousting (3) ASS ASkS
17 A fantastic rent for cavern (5) ANTRE {A}{RENT*}
19 The world is round basically with large spin (5) TWIRL {The}{Wo..d}{Is}{Ro..d}{L}
23 Extra publicity by gangster! (3-2) ADD-ON {AD}{DON}
24 Money in petroleum (3) LEU [HIPS]
26 Live to party endlessly by pool (5) DWELL {Do}{WELL}
28 Hard one put in cryptic grid (5) RIGID {R{1}GID*}
29 Common tin perhaps for vegetarian (7) AVERAGE {AVERAGE+TIN}*=VEGETARIAN
31 British rich flying around on world's busiest airways! (7) BRONCHI {B}{R{ON}CHI*}
33 & 34 Voter list and EC role? Lost all fights! (9,5) ELECTORAL ROLLS* One R less in Fodder
34 See 33
DOWN
1 Passing test mostly or fairly passing now and then (9) TEMPORARY {TEMPt}{OR}{fAiRlY}
2 Cosmetics part reportedly going to derelict son (4-3) ROLL-ONS {(~role)ROLL}{SON*}
3 Seek women's love with love (3) WOO {W}{0}{0}
4 Daydream about holding back President! (5) OBAMA [T<=]
6 Crude criminal giving up diamonds for wife (5) BAWDY BA(-d+w)WDY
7 An Asian at fights for fat Ghanaian (7) AFGHANI {AFGHANI+AN+AT}*=FAT GHANAIAN
8 Untidy, tidy or finally untidy! (5) DIRTY {TIDY+oR}*
12 Land of honest men (5) REALM {REAL}{M}
14 Rear line (5) BREED [DD]
18 Time to relax or tantalise (5) TEASE {T}{EASE}
19 Ultimately laserjet printer has one inside! (5) TONER {l..eT}{p...eR} over {ONE} &lit
20 The one in Paris, removes water for dirty clothes (9) LAUNDRIES {LA}{UN}{DRIES}
25 Time for large plan, say (5) STATE S(-l+t)TATE
26 Traded in homemade altarpieces (5) DEALT [T]
27 Progressive artist ignored slander (5) LIBEL LIBEraL
30 Sin in locker room (3) ERR [T]
32 Paddle board on the inside (3) OAR [HIPS]
Reference List
Men = M, Party = DO, America = A, English = E, King = K, Large = L, Small = S, Time = T, British = B, Women = W, Diamonds = D, Wife = W, The and one in French = LA, UN, Artist = RA
