UPDATE, 3:30 p.m. ET: RIM just held a conference call for reporters, with David Yach, its chief technology officer for software, saying the problem originated Monday in Europe — and spread, he said, simply because there was such a massive backlog of emails that had built up.

“That’s why we’re seeing effects around the world,” he said.

Yach promised that every message sent during the outage would eventually be delivered — though obviously many of them will be dated by the time they eventually arrive.

Customers are not mollified. The complaints keep coming, with “Dear BlackBerry” now a trending term on Twitter.

A sampling in the last few minutes:

“Dear BlackBerry, Thanks for the new customers. Sincerely, iPhone.”

“Dear #BlackBerry what do you think about iPhone? How much is it? I think you and me … our relationship … uumm … it’s over, loser!!”

“Dear BlackBerry, I think you should compensate us for our loss “

So what about making it up to people? A reporter asked. Yach sounded a bit thrown. “We’re just concentrating on getting things back up and running. Make-goods? I don’t have an answer for that right now.”

Original story, 10: 34 a.m. ET: Does your BlackBerry work today? Research in Motion, whose BlackBerry service has had reported outages in Europe, the Middle East, Africa and parts of Asia already this week, acknowledged problems with North American services today as well.

This morning there were widespread complaints of outages in the United States. The company, headquartered in Canada, confirmed that the problems here are similar to what it had seen in other parts of the world.

“BlackBerry subscribers in the Americas may be experiencing intermittent service delays this morning,” RIM said in a statement. “We are working to resolve the situation as quickly as possible, and we apologize to our customers for any inconvenience. We will provide a further update as soon as more information is available.”

BlackBerry has had transmission problems on other continents for three days now. It said a critical part of its communication system was down, and a backup system wasn’t working either.

“Message delays were caused by a core switch failure in RIM’s infrastructure,” the company said on Twitter late Tuesday. “Now being resolved. Sorry for inconvenience.”

Among the snarky replies: “Dear BlackBerry, I think it’s nice that you’re honouring Steve Jobs’ death with a 3 day silence.”

The company’s timing stinks. It still has the dominant smartphone operating system worldwide but has slipped to No. 3 in the U.S. and is quickly losing market share to Google’s Android and to Apple, according to the market research firm ComScore statistics.

In the U.S., Android had 44 percent of the U.S. market as of August, up 5 points since the beginning of May. Apple rose 1 percent to the No. 2 position, with 27 percent. RIM dropped 5 percent, to 25 percent.

RIM stock, if you’re an investor, has dropped from $70.54 per share in February to $23.88 this afternoon. There’s a shareholder group, led by the firm Jaguar Financial, calling for a change in management.

All of which gains steam when jokes like this are retweeted on Twitter:

“What did one BlackBerry user say to the other BlackBerry user?

“Nothing.”