Aven Mimeomancer — ruling 1

The effect from the ability overwrites other effects that set power and/or toughness if and only if those effects existed before the ability resolved. It will not overwrite effects that modify power or toughness (whether from a static ability, counters, or a resolved spell or ability), nor will it overwrite effects that set power and toughness which come into existence after the ability resolves. Effects that switch the creature's power and toughness are always applied after any other power or toughness changing effects, including this one, regardless of the order in which they are created.

Aven Mimeomancer — ruling 2

If the second ability affects a creature, it doesn't cause that creature to lose any of its abilities. It just gives that creature flying as well.

Aven Mimeomancer — ruling 3

The affected creature remains 3/1 and has flying as long as it has a feather counter on it. The effect continues even if Aven Mimeomancer leaves the battlefield.

Aven Mimeomancer — ruling 4

You may put a feather counter on a creature that already has a feather counter on it. Doing so has no visible effect unless some other effect has changed the creature's power or toughness, or caused it to lose flying, since the last feather counter was put on it.

Aven Mimeomancer — ruling 5

If all feather counters on a creature are moved to a different creature, the ability doesn't follow them. The first creature stops being affected by the ability because it no longer has a feather counter on it. The second creature is not affected by the ability because Aven Mimeomancer didn't target it.

Aven Mimeomancer : règles, fonctionnement et interactions (MTG)

Aven Mimeomancer is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

Flying At the beginning of your upkeep, you may put a feather counter on target creature. If you do, that creature has base power and toughness 3/1 and has flying for as long as it has a feather counter on it.

How it works : Aven Mimeomancer

Original English text — Wizards of the Coast / Scryfall

#1October 1, 2009· Wizards of the Coast
The effect from the ability overwrites other effects that set power and/or toughness if and only if those effects existed before the ability resolved. It will not overwrite effects that modify power or toughness (whether from a static ability, counters, or a resolved spell or ability), nor will it overwrite effects that set power and toughness which come into existence after the ability resolves. Effects that switch the creature's power and toughness are always applied after any other power or toughness changing effects, including this one, regardless of the order in which they are created.
No other card is named in this ruling.
#2May 1, 2009· Wizards of the Coast
If the second ability affects a creature, it doesn't cause that creature to lose any of its abilities. It just gives that creature flying as well.
No other card is named in this ruling.
#3May 1, 2009· Wizards of the Coast
The affected creature remains 3/1 and has flying as long as it has a feather counter on it. The effect continues even if Aven Mimeomancer leaves the battlefield.
No other card is named in this ruling.
#4May 1, 2009· Wizards of the Coast
You may put a feather counter on a creature that already has a feather counter on it. Doing so has no visible effect unless some other effect has changed the creature's power or toughness, or caused it to lose flying, since the last feather counter was put on it.
No other card is named in this ruling.
#5May 1, 2009· Wizards of the Coast
If all feather counters on a creature are moved to a different creature, the ability doesn't follow them. The first creature stops being affected by the ability because it no longer has a feather counter on it. The second creature is not affected by the ability because Aven Mimeomancer didn't target it.
No other card is named in this ruling.