Skullbriar, the Walking Grave

The counters that remain on Skullbriar as it changes zones aren't "placed" on Skullbriar. Effects like Doubling Season's and Melira, Sylvok Outcast's won't affect those counters.

Skullbriar's last ability only works if it has that ability in the zone it's moving from. For example, with Yixlid Jailer ("Cards in graveyards lose all abilities") on the battlefield, a Skullbriar with a counter on it in a graveyard loses that counter when it's put onto the battlefield. Conversely, that Skullbriar moving from the graveyard to the battlefield would retain that counter if Humility ("All creatures lose all abilities and are 1/1") were on the battlefield; if Skullbriar then left the battlefield with Humility still on the battlefield, it would lose the counter.

Counters that adjust power and/or toughness affect Skullbriar's power and/or toughness in zones other than the battlefield. For example, a Skullbriar in the command zone with a +1/+1 counter on it will be 2/2.