A methodical and scientific approach of ending a relationship without the other person knowing. This method attempts to leave the post phase out relationship civil for both parties. If starting from a romantic relationship results often end in a casual friendship that can continue for years. Results vary based on expertise. The phase out is based on the principle that anything can be accomplished gradually. It's related to the old science experiment that a frog thrown into hot water will go into shock but a frog left in a pot that is warmed will be fine.
To accomplish a successful phase out, the phaser (person performing the phase out) must evaluate the relationship with the phasee (person being phased out) and arrive at an appropriately paced schedule. No two phase outs are exactly the same, because all relationships are different, but luckily they all use similar steps. The basic rule is to gradually reduce contact (phone, IM, physical) but not in huge jumps. Over the period of two months almost anyone can be phased out. When it comes to the actual breakup, it will often seem so natural to the phasee that they feel it was their idea.
Are you still with your girlfriend? Actually no, I performed a phase out on her about two months ago. We hung out last week though.