Morgan Stanley’s Katy Huberty, whose Apple (AAPL) forecasts have turned increasingly bullish in the past year (see Morgan Stanley drinks the Apple Kool-Aid), issued a report Friday even more optimistic than the glowing note she published last November.

In her “bull case” scenario, Apple ships 87 million iPhones and 65 million iPads in calendar 2011, driving its stock to $540 a share by November 2011. By 2013, she has Apple shipping 178 million iPhones and 120 million iPads.

“We believe Apple offers the most attractive valuation in our large cap tech coverage, with potential for 34% revenue and 41% EPS [compound annual growth] through 2013,” she writes. “In our view, the market is far too near-term focused and the current valuation – 15x CY2011 P/E – suggests that the market questions the company’s long-term growth potential. We disagree.”

In Huberty’s view, the traders who are keeping Apple’s stock down — it closed Thursday at $344.97 — are missing four potential catalysts for growth:

• Expanding distribution in China
• Lower-priced iPhones in 2012
• Ever greater tablet market, with continued Apple dominance
• A new Smart TV product category in 2012-13

In Huberty’s “base case,” in which Apple sells only 72 million iPhones and 30 million iPads in 2011, the stock still hits $410 by November. In her “bear case,” lower margins and growing concern about Steve Jobs’ health drive the stock down to $270.

Huberty’s three-scenario approach gives her a lot of flexibility, but tends to make her look bad at the end of each quarter when Apple blows past her base case numbers. In a comparison published in January of how much better or worse analysts were doing at predicting Apple’s earnings over the past two quarters, Huberty came in dead last, with an error reduction of -32.7%.

Also on Fortune.com:

• Apple analysts: Who’s getting better, who’s getting worse
• Morgan Stanley’s ‘bull case’ for Apple: 80 million iPhones, $500 a share
• Morgan Stanley drinks the Apple Kool-Aid

[Follow Philip Elmer-DeWitt on Twitter @philiped]