Turntable versus tonearm versus cartridge: which is MOST important?

Raul, no sensible audiophile could disagree with what you wrote. (Is the term “sensible audiophile” an oxymoron?) But at the outset, the OP wrote that he did not want responses to the effect that everything is important. This I think drove the tenor of the responses he’s gotten. I dislike such questions per se, but I was bored enough at that moment to concoct a response. With an excellent TT and tonearm, you can get a lot of juice out of a mediocre cartridge, but I don’t think the reverse is true. Not in my experience.

@chakster
"I’ll tell you more: change the stylus tip on your cartridge and you will change the whole sound."
I agree completely. I just re-tipped the Zyx Omega G cartridge and the sound is completely different with the original. Better or worse is another story.

Never mind , transducers always are the most important links in any audio system.

Raul, anyone who has ever spent ten seconds on this Board in the last ten years knows you have a unrequited out of control cartridge fetish. I envision you sleeping on a mattress surrounded by cartridge boxes. 

Transducers are not the most important part of the audio system. You may believe so and you have every right to your belief but many argue otherwise, and I am among the latter camp. Look up Herb Reichert's recent tale of wandering into an audio store and being introduced to Naim gear set up with inexpensive loudspeakers for a good anecdotal account of the opposing view. 
Cartridges and loudspeakers are very simple devices. Only audiophiles make them out to be more complicated and exotic than they really are. Do they have the biggest influence on sound character? That is a different question. Sorta like are noses the most dominant feature on a face? Yeah, most times and certainly on mine! That does not make them the most critical component. 
Feed a pair of the most expensive loudspeaker on the planet (any of the top 50) with a mediocre amplifier and preamplifier and you can never get anything better than mediocre to good sound. Pair a pedestrian set of loudspeakers (critically positioned in the room they are in) up with a stellar amp and pre-amp and you can get great sound. 
Which brings us back to the current debate which has surfaced time and time again. Like my nose joke, turntables get the most attention because-imho-they are the most prominent item. The choice of drive unit is almost inevitably made first. It draws all the attention of would-be buyers. Ooooh, look at that huge platter! Ooooh, look at that outboard power supply with a digital read out! You get the idea. Most of us are guilty of that misdirected (again, must my humble op) focus. 
I am biased perhaps because I got off the modern era table bandwagon and went to vintage with Reed 3P arms though I have spent considerable money on cartridges. But I know that could give up those cartridges and mount a $250 Audio Technica or Denon and get fantastic sound. 

Tube power supply for TT ;-)

now, we are talking……

The cartridge!
For sure, to get the most out of a cartridge, there needs to be good arm and TT. IME, there was excellent improvement when I upgraded my TT and arm, but my new top line cart gave the most dramatic and transformative change in SQ… by far.