Here's a sentence:
My girlfriend walked into the bedroom and caught me m__________ating.*
After all the previous ruction (see the ever-growing comment thread under that post) over "me" versus "my," you might wonder whether the above sentence should be changed to "caught my m__________ating."
No. The above sentence is perfectly correct. Why? Because the word m__________ating, in the above context, is a participle, not a gerund. M__________ating is short for in the process of m__________ating. (And may that be the only thing that's short.)
Participles are interesting in that they can also function as adjectives and adverbs.
Greg's hapkido move sent Rick flying.
(participial adverb: how was Rick sent?)
The blubbering gladiator shouted for his puppy.
(participial adjective describing gladiator)
So be careful. Make sure you're dealing with a gerund before you stick a possessive in front of it. If it's a participle, you might be safe using an object pronoun in the accusative (direct-object) or dative (indirect-object) case.
Noticed the hyphens inside the parentheticals? As a rule of thumb, you hyphenate phrasal adjectives when they precede the nouns they modify. This isn't always the case, however, if leaving out the hyphen creates no ambiguity. If a hyphenless locution is clear in its meaning, don't hyphenate.
Regarding ambiguity and hyphenation, here's the classic example:
(a) a violent weather seminar
(b) a violent-weather seminar
If you're talking about a seminar on violent weather, then (b) is what you write. If you're talking about a weather-related seminar that turned into a brawl, then (a) is potentially better, but keep in mind that leaving out the hyphen creates an ambiguity as to which seminar you're talking about—one that was about storms or one that turned violent.
Another interesting example of hyphenation with phrasal adjectives comes from how to handle ethnicity: it's "African-American studies," not "African American studies," consistent with the aforementioned rule. From Wikipedia, this inspiring 1915 speech by Teddy Roosevelt:
There is no room in this country for hyphenated Americanism. When I refer to hyphenated Americans, I do not refer to naturalized Americans. Some of the very best Americans I have ever known were naturalized Americans, Americans born abroad. But a hyphenated American is not an American at all … The one absolutely certain way of bringing this nation to ruin, of preventing all possibility of its continuing to be a nation at all, would be to permit it to become a tangle of squabbling nationalities, an intricate knot of German-Americans, Irish-Americans, English-Americans, French-Americans, Scandinavian-Americans or Italian-Americans, each preserving its separate nationality, each at heart feeling more sympathy with Europeans of that nationality, than with the other citizens of the American Republic … There is no such thing as a hyphenated American who is a good American. The only man who is a good American is the man who is an American and nothing else.
Note, though, that ethnicity tends not to be hyphenated when it's nominal (i.e., being used as a noun or noun phrase), so the writer of the above words was hyphenating incorrectly.
Trivia: Theodore Roosevelt has the bizarre distinction of proudly wearing two seemingly contradictory (to modern eyes) political labels: "Republican" and "Progressive." I guess that's evidence that language does change over time, eh? (Cf. the use of the terms "public school" and "private school" in UK versus US English. Sometimes it's not so much diachronic change as it is synchronic change.)
*For all you know, "m__________ating" might refer to
1. masturbating (if you have a dirty mind)
2. masticating (chewing)
4. medicating (i.e., self-medicating)
5. micturating (urinating)
—or any of these other words:
maneating, manhating, manipulating, marinating, mating, matriculating, meateating, mediating, migrating, misallocating, misappropriating, misdating, misstating, mistreating, mitigating, moderating, modulating, motivating, motorboating, mutating, mutilating
I like the idea that my girlfriend caught me mutating.