And with good reason. iPhone sales remain the company’s single biggest source of revenue — 52.6% of total revenues, to be specific, at this time last year.

In a note issued Wednesday, Bernstein’s Toni Sacconaghi rattled off a list of imponderables that are pulling his iPhone unit sales estimate (38.8 million) in several different directions:

• Slower sales than expected to China Mobile (CHL)
• Tighter carrier upgrade policies in the U.S.
• Strong demand in emerging markets for the older (and cheaper) iPhone 4 and 4S.

“Combined,” he writes, “these factors lead us to believe there is more downside risk than upside risk to our estimates.”

On the other hand, Morgan Stanley’s Katy Huberty reported Thursday that her AlphaWise smartphone tracker, which gathers sell-through data by analyzing Web searches, indicates iPhone demand at 40.6 million units, well above her 38 million estimate. “Recent promotions,” she writes, “like those at U.S. carriers and retailers, and product adjustments, notably the introduction of an 8GB iPhone 5c in some regions, may have stimulated demand more than expected.”

It’s certainly more than expected by most of the analysts we polled in our quarterly survey, now in its sixth year.

We’ve heard from 32 Apple analysts so far — 20 Wall Street professionals and 12 amateurs. Their estimates range from a high of 42.5 million iPhones, from Needham’s Charlie Wolf, to a low of 34.05 million from a pro who asked that his name and affiliation not be used. He’s one of 10 analysts who believe Apple sold fewer iPhone last quarter than the 37.4 million it sold in the same quarter last year.

The average of all the estimates is 38.2 million, which would represent a 2% increase year over year. As usual, the amateurs are more bullish, with an average estimate of 38.8 million. But the pros are right behind them at 37.8 million.

We’ll find out who was closest to the mark when Apple reports its fiscal Q2 2014 earnings after the markets close on Wednesday, April 23.

Below: The individual analyst’s estimates — pros in blue, indies in green. Thanks as always to Posts at Eventide‘s Robert Paul Leitao for pulling together the Braeburn Group numbers.