I heard that the time for submitting presidential election papers passed on March 3, 2016.
No one seems to have registered by then.
How could a third party (Romney, Bloomberg, Trump) run as an independent or other party candidate now?
There is no date associated with registering as a candidate for federal office. Some states' branches of the main parties have had recent deadlines, but none on March 3 that I can see.
In fact, you don't have to register at all unless you have received contributions or made expenditures over $5,000.
As an example from this Slate article:
In the 1996 presidential campaign, Ralph Nader made a point of not filing a statement of candidacy; he came in fourth in the voting.
See the Federal Election Commission website for more details on the requirements.
The per-state deadlines are important, of course; a write-in candidate wouldn't want to lose out on California by waiting till after May 17, for example.
Another issue is that third parties don't necessarily need to register the same way as independents. Some of them have ballot access for their candidates in some states regardless. Or they may have been able to register a spot without selecting a specific candidate.
See https://www.lp.org/2016-presidential-ballot-access-map for example. The libertarian candidate will appear in California, Texas, and Florida, the three states with the most electoral college votes. They still have to do work to get their candidate exposed in states including New York, Illinois, and Pennsylvania (the next three states). It may be that in the latter states, that they have to register the same as independents do. Or there could be other issues.
Presumably other parties have similar experiences. I picked the libertarians because I knew they have had a lot of success in getting listed in past elections.