Shares in Apple Inc. (AAPL) set another closing high on Tuesday, ending the day at $ 456.48, a gain of $3.47 (+0.77%), on moderately light volume of 14 million shares trading hands. That puts the company’s market capitalization at $425.6 billion, lengthening Apple’s current lead as the world’s most valuable company.

Apple and energy giant Exxon Mobil have been battling it out during much of the last year for the title of world’s most valuable company, but Apple retook the lead shortly after the company’s Q1 2012 financial results were announced on January 24th, as shown in the chart below.

AAPL vs. XOM during the last 90 days

Exxon Mobil’s stock (XOM) ended Tuesday’s trading session at $83.74, down $1.75 (-2.05%), on heavy volume of 27.2 million shares trading hands. That gives the company a market cap of some $401.4 billion.

There’s nothing at stake for having this title, and in the grand scheme of things, it doesn’t really matter a hill of beans which company is worth more. For long time Apple watchers, however—not to mention list lovers and those obsessed with ranking such things—the idea that Wall Street might value Apple above all other companies can be quite interesting.

With 4.8 billion shares outstanding for Exxon Mobil and 932.4 million shares outstanding for Apple, small movements in both stocks can make for large changes in their relative valuations.

Whatever the case, it’s likely that it will be one of these two companies that will be first to cross the half-trillion dollar mark in valuation. The only real question is how long it will take.

*In the interest of full disclosure, the author holds a tiny, almost insignificant share in AAPL stock that was not an influence in the creation of this article.